# rationalizing the denominator with conjugates worksheet pdf

2+3 b. Rationalizing Denominators Containing Two Terms Radical expressions that involve the sum and the difference of the same two terms are called conjugates. 2+3 b. Rationalizing the Denominator Recall: for . Rationalizing Denominators: Index 3 or Higher; With Variables Simplify. Instead we will use what is called a conjugate. I. Examples of conjugates are 1a - 2b and 1a + 2b x + 1y andx - 1y EXAMPLE 4 Rationalize each denominator. Multiply the numerator and denominator by the given radical to have a rational number in the denominator, and further simplify the expression. square root of 8 is 2 rad 2) for some of the problems. How to Rationalize Denominators That Contain Radicals - Fractions are easy to solve, be it addition, subtraction, multiplication, or even division. Case III: There are TWO TERMS in the denominator. Reduce. 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Some of the worksheets for this concept are Radicals, Rationalize the denominator and multiply with radicals, Rationalizing a denominator, Rationalize the denominator, Radical workshop index or root radicand, Rationalizing imaginary denominators, Dividing radical, Chapter 5 complex numbers. Title: Microsoft Word - rationalize-denominator-1 … d) √1. Step 2: Multiply the numerator and denominator by the conjugate. Multiply by a convenient form of 1 with the conjugate. stream Worksheet Rationalize the denominator and multiply with Radicals Rationalizing is done to remove the radical from the denominator of a fraction. The only diﬀerence is we will have to dis tribute in the numerator. Example: the conjugate … There are twenty-four problems on this practice, so it will take the students about 30 minutes to complete. Customary units worksheet. The Career Account database server will be down on Saturday December 19 from 4pm to 10pm. •¹³ÑEå«é>5›ç]^?˜¹mêzïä~^@åïÈqN&à\A ış#:Lwc‚Qİ£‡—Õw¡çI!ô=üo¨¥¾‚ú—ï±ğ MORE RATIONALIZING THE DENOMINATOR: (DIVISION) If the denominator contains two terms such that at least one term has a radical, multiply the numerator and the denominator by the conjugate of the denominator: Conjugate – the conjugate of a binomial of the form 96 : is 95 :. Denominators with two terms Multiply the numerator and denominator by the conjugate of the denominator. Reduce. By the end of the lesson, they should be able to rationalize a denominator even if it contains complex or imaginary numbers. Rationalizing the Denominator Recall: for . endobj �n���&�����g���|�LY>��-�K=��zTz�?��(K�8��梇�7*k�-X�VI��Z�E�Te��y� �]B��s �M�4-4�QR���#�:X�O� R |Nw�� �����g'��mt�l�� @y�\�iV� ��ĥ��2q�:�[I��"��;�н�����ܒ�X%v=�(�}pd}�m�#ەӸh�t~����}��|�%��Iz��>���nÍ�zV�Ҙm9F��;ϰ�f��0���6��j�K�>��/����5��h�y���U��x�׃�jK�\�"|��n;u�8�����G��^���B,aw2L�Mn�����P�. So for our example with 3 √ − 5 in the denominator, the conjugate would be 3 √ + 5. Multiply and Divide Radicals 1 Multiple Choice. Complementary and supplementary word problems worksheet. Step 1: Find the conjugate (it’s the denominator with different sign between the two terms. o 9 lM da gdCes Fwoi5toh l 5IGnJf dian9i Ztwe2 HAHl Rgveob3r na4 61 J.U Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Dividing Radical Expressions Date_____ Period____ Simplify. And now lets rationalize this. m Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Rationalizing Imaginary Denominators Date_____ Period____ Step 2: Distribute (or FOIL) both the numerator and the denominator. Make sure to distribute or FOIL the numerator and denominator. 1 23 7 b. To link to this page, copy the following code to your site: View Homework Help - rationalize-the-denominator-worksheet.pdf from MATH 1B at Santa Rosa Junior College. However, none of the problems involve using conjugates. <> 5−35 c. 3x−3 To rationalize a denominator that contains two terms, multiply both 4-3-Worksheet by Kuta Software LLC Answers to Rationalizing the denominator: Square Roots Displaying top 8 worksheets found for - Conjugates Rationalize. 2! P.3.6 Rationalizing Denominators & Conjugates 1) ... .C B 9AlTl E 3rxi2g VhStQsm crQegs7ejr DvaeOdb.O Q wMVaPd7e e rwvi 2tKhI RISnjf Kikn4i gt DeP GAnl9gse 1b JrPaD O2R.l Worksheet by Kuta Software LLC 15) (2 + 3)(2 − 3) −7 ... Worksheet- Rationalizing the Denominator with Binomials and Key.pdf Rationalizing Denominators Worksheets How to Rationalize Denominators That Contain Radicals - Fractions are easy to solve, be it addition, subtraction, multiplication, or even division. Rationalizing Denominators Containing Two Terms Radical expressions that involve the sum and the difference of the same two terms are called conjugates. P.3.6 Rationalizing Denominators & Conjugates 1) NOTES: ... square root of a perfect square in the denominator. 3225 24x c. A 3 2 9 CONCEPT CHECK Determine by which number both the numerator and denominator can be multiplied to rationalize the denominator of the radical expression. Comparing rates worksheet. Work your way through these pdf worksheets to hone your skills in rationalizing the denominators. The solutions look really similar, so the student must watch what they are doing. In this lesson, students will learn how to rationalize the denominator and will be re-introduced to the idea of a conjugate and also imaginary numbers. Denominators with two terms Multiply the numerator and denominator by the conjugate of the denominator. This self checking worksheet features rationalizing of the denominator. Rationalizing Denominators Worksheets. Career Account web sites will be available during this window, but applications that use a database (such as WordPress or phpBB) will not work correctly. Assume that all variables are positive. The advantage of a conjugate is when we multiply them together we have ( 3 √ − 5)( 3 √ + 5), which is a sum and a diﬀerence. Remember to find the conjugate all you have to do is change the sign between the two terms. We will consider three cases involving square roots. 26 + 2 25 - 23 c. 22m 32x + 2m Solution a. Note: Squaring a radical will eliminate the radical. I. for any a and b. are conjugates. So our current method will not work. A conjugate is made up of the same terms, with the opposite sign in the middle. Example 3: Find the conjugate of each expression. 5. The conjugate is the same two terms but with a different sign between them. Metric units worksheet. This is the key to Topic 23 Worksheet Radicals Extra 17; Rationalizing the denominator using conjugates. #�:��_@�Aa�hL�^I��. ì ë ì is our final answer. Rationalizing Imaginary Denominators. Step 2: Distribute (or FOIL) both the numerator and the denominator. Then simplify. Examples of rationalizing the denominator. Step 3: Simplify if needed. Rationalizing Imaginary Denominators Rationalizing Imaginary Denominators – Example 1: Since the conjugate for this numerator is 4 + 5 , we will multiply top and bottom by that number. 1 24 8 PRACTICE EXAMPLE 2 Rationalize the denominator of A 7x 3y. %PDF-1.4 Examples Simplify. Each question corresponds to a matching answer that gets c { €÷�H­»Â�k?�M“³ü”Ş+ ~:zïÕ?0p!Úym|Ã»”Åc”3t®ßÀ1¶|á‰ğ\$Â>•^TcSË½ÜN£e¡=M¤ƒqOL5ïõó­ÿ3`èç3ŒÎÑ7¦•[õ7Œ�VÂ§½Üfüø *Cancel out the 3’s in both the numerator and denominator Because we cannot simplify any further, √7 ë / . By using this website, you agree to our Cookie Policy. Case III: There are TWO TERMS in the denominator. Free worksheet(pdf) and answer key on rationalizing the denominator. ©G 32v071 d2N 2KOuutiaG MSHoyfNt4wGagr 5ec JL 7L pC W.f H pAQlRlB BrGiAgvh4t Rsd 4rgeUseSr tvye Rdy. Example 1: Multiply by a convenient form of 1. Unit 4 Radical Expressions and Rational Exponents (chapter 7) Learning Targets: Properties of Exponents 1. Solution Use the quotient rule. This quiz and worksheet combo will help you test your understanding of this process. stream Rationalizing Denominators And Conjugates - Displaying top 8 worksheets found for this concept.. Answer: Example 2: Find the conjugate of . You rationalize it. x��Y�r��y~���mZ]�} �R�r�b�D(D�H����/k묞�(譲ry�2+��I Make sure to distribute or FOIL the numerator and denominator. 5−35 c. 3x−3 To rationalize a denominator that contains two terms, multiply both Some rationalize with a variable and some do not. ! Metric units worksheet. Mensuration worksheets. There is a more efficient way to find the ℎ root by using the exponent rule but first let’s learn a different method of prime factorization to factor a large number to help us break down a large number D. SIMPLIFY RADICALS WITH PERFECT PRINCIPAL ROOT USING EXPONENT RULE . ¨¸ ¨ ©¹ Distribute in the numerator; multiply conjugates in the denominator. A conjugate is made up of the same terms, with the opposite sign in the middle. Example 3: Find the conjugate of each expression. Area and perimeter worksheets. 27 0 obj '���)M�>�0^���::� But do you know how to work with fractions that have radicals in their denominators, yes! Simplify by rationalizing the denominator. Complementary and supplementary worksheet. Q1: Given that = 5 √ 7 − √ 2 and = √ 7 − √ 2 , find + expressing your answer in simplest form. not cleared the radical, only moved it to another part of the denominator. Simplify. Rationalize the Denominators - Level 1. 5 0 obj Rationalizing the Denominator Worksheet. RATIONALIZING THE DENOMINATOR WORKSHEET. endobj Free rationalize denominator calculator - rationalize denominator of radical and complex fractions step-by-step This website uses cookies to ensure you get the best experience. a. 5I���_��~������%'�hU�n���}~(�g�Ջ���P��������+H�S�ko���E��(�8/N�`�:�Y�d�������6�����ʋd�8�� �i�V-�tu A��EA�R���Fxo���R����y����%������7���y1����'��V��/��K-TJ��;/^8/�>��}VG���u+,RJ���U�R� {���P�����K\(��n^��*���Mk�Ik'��:hO�.&:X#Lr��_Ox�������a������1��k��'5H�bMȷ�f�D� m Model Problems In these examples we will practice rationalizing the denominator. 1) a2 3 a 2) 1 4 3x 3) 2m 4 2m 4) x2 4 3x 5) 2u 3 u 6) 7 3 x 7) n 3 n 8) 3 4 x 9) 8 3 3x2 10) r 4 3r3 11) −4 + 3 v2 3 v 12) −6 + 3 x2 3 5x 13) −2 − 4 a 4 a3 14) −3 + 4 … Step by step guide to rationalizing Imaginary Denominators. a. In this worksheet, we will practice rationalizing denominators of radicals. Geometry worksheets. Students need to know how to simplify radicals (i.e. 2331 Then simplify. The best way to get this radical out of the denominator is just multiply the numerator and the denominator by the principle square root of 2. *Cancel out the 3’s in both the numerator and denominator Because we cannot simplify any further, √7 ë / . Multiply by a convenient form of 1 with the conjugate. Area and perimeter worksheets. 5 23 b. Simplify. Example 1: Multiply by a convenient form of 1. Multiply the numerator and denominator by the given radical to have a rational number in the denominator, and further simplify the expression. Answer: }p�ā��/�\�3���ӧ�g� ��}쇱�kջ%oE>e9 7w~�o۩����P`��#[/�u�9U��jL����Q�;endstream It is 1 square roots of 2. Double facts worksheets. Career Account web sites will be available during this window, but applications that use a database (such as WordPress or phpBB) will not work correctly. D p 9a tlplw nrgi0g ih 0t zsm r2elsteurgvweed 4 8 p 3 6 rationalizing denominators conjugates. Some of the worksheets for this concept are Radicals, Rationalize the denominator and multiply with radicals, Rationalize the denominator, Rationalize the denominators 1, Radical expressions rationalizing denominators and, Rationalizing a denominator, Dividing radical, Grade 9 simplifying radical expressions. Displaying top 8 worksheets found for - Rationalizing Denominators And Conjugates. ����S9������n6S��^�s���_�藘=i�����R�]�Eۗf���]�;1>�� ��'��4������T {x��,8 �!8���&ґ{�_6��a�HP^�,P����vC��v�L�Kp��ԮO��K��:�ҁ6:gd�{���! Remember to find the conjugate all you have to do is change the sign between the two terms. a. a. Showing top 8 worksheets in the category - Rationalizing Denominators And Conjugates. Rationalize the Denominators - Level 1. Since the conjugate for this numerator is 4 + 5 , we will multiply top and bottom by that number. Step 3: Simplify if needed. Missing addend worksheets. 25 scaffolded questions that include model problems and a few challenge questions at the end. Worksheet given in this section is much useful to the students who would like to practice problems on rationalizing the denominator. ºö ¯+ˆGıOÌ�j`&¤q¹~DsosÀX@¾vÿÇ}Ü#p=Ÿv÷,ÑXkÒæ%ª¸ó^oĞÓ¢j[MÎ�µX�GÙ£&K:�C�NáÄÉmN~‚ô­4�D…ú®B]´µyµ]Mg`•Ì±¸êğ{TœÎû¢ãù>=§TÕÍ(ıÛo1~ §¤(7`y/×*4¡ş]z¨¢ãQ¥?ù¶oÎüÆ¾ıˆ2 e‰ˆçào8ÁÊdˆ¾Éğu`òºÍ]Cr2�ïv0|°ûØ›Ş4Ìñ 8j@[²áôÑ£öE?¬~œQ¢hkQv�ßÍ Oâ¢wë®);Ùµ»t1˜yÇœ Ë:ƒŒVçS\ èkÅè �d¸Gœ×§S\¥9Ö‘ÇFSåÈÜğµ7ZÔšŞô å&e¡si€VĞ0B‚6&��Ê œ2&|NIds's7°In°Œ7�)Cè¾¹�†­y”¸5ø�CgÈ7Êkô”0ŠˆšLÌ�ïÃgV|ÎY#"ˆš¤/4ñi—>—”(‘oT�ÏÕæG¹k�¢‰åÚÒÛMıÍ îùsÓçÒ›¾8­©ğ­ Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Step 1: To rationalize the denominator, you must multiply both the numerator and the denominator by the conjugate of the denominator. This worksheet also helps my students to … %�쏢 Mensuration worksheets. Sum of the angles in a triangle is 180 degree worksheet. Because of the expression y + √(x 2 +y 2) in the denominator, multiply numerator and denominator by its conjugate y - √(x 2 + y 2) to obtain Questions With Answers Rationalize the denominators of the following expressions and simplify if possible. How to rationalize the Denominator with conjugates, step by step examples, and many practice problems solved step by step. Model Problems In these examples we will practice rationalizing the denominator. a. F worksheet by kuta software llc math for college readiness name date period 2 a2g0f1t4 r pk mustead ys5ohfxt lw ia br8ew qlflrc x. �x��j}؋8���\���26�:��F�Kk�/��ﲈ�9S�V�����Fg/����ci��["���Rjk�i��� �鼘i�y��a�@?�(����7��5��Ϣ���z*�]��2%W��C�0%W�}fA�} So for our example with 3 √ − 5 in the denominator, the conjugate … Rationalizing Denominators And Conjugates - Displaying top 8 worksheets found for this concept.. After the Warm Up activity, for Independent Practice I give my students a Rationalizing Denominators Worksheet. To rationalize the denominator, multiply the conjugate of the denominator to both the numerator and denominator and simplify the expressions using the FOIL method. Missing addend worksheets. ©Q h2 n0q1 w3R VK9u Utja j ZSpodf Ftxw pa arDeD mLaL7CV.H J 8AVlElk 6rciPgVh6t QsU zr ie ms re 9r sv4e Fdk. MORE RATIONALIZING THE DENOMINATOR: (DIVISION) If the denominator contains two terms such that at least one term has a radical, multiply the numerator and the denominator by the conjugate of the denominator: Conjugate – the conjugate of a binomial of the form 96 : is 95 :. Answer: <> Work your way through these pdf worksheets to hone your skills in rationalizing the denominators. The following step-by-step guide helps you learn how to rationalize imaginary denominators. Rationalizing denominators with radical expressions requires movement of this denominator to the numerator. Reduce. Complementary and supplementary worksheet. I can use properties of exponents to simplify expressions. Rationalizing the denominator; ... .C B 9AlTl E 3r xi2g VhStQsm crQegs7ejr DvaeOdb.O Q wMVaPd7e e rwvi 2tKhI RISnjf Kikn4i gt DeP GAnl9gse 1b JrPaD O2R.l Worksheet by Kuta Software LLC 15) (2 + 3)(2 − 3) −7 6 0 obj Example: the conjugate … Student Name: _____ Score: Printable Math Worksheets @ www.mathworksheets4kids.com 1 3 Answer: 3 5 Answer: 2 3 Answer: 1 2 2 Answer: 7 11 Answer: Rationalize the Denominator Answer key . Complementary and supplementary word problems worksheet. Free worksheet pdf and answer key on rationalizing the denominator. Database Downtime. Step by step guide to rationalizing Imaginary Denominators. Database Downtime. ©l s2 n0E1Q1J 9K eu ZtEa T 3Siojf Xtpw ZaYrJe Z cLTLzC k.U K yAVljl l lr1i vg thCt ysD Drqe 4s qe rMvRe5dW.b F dM sa 1d 1eL wBi4t9h 2 wI9nif niknLi lt peS hAWlag9e berBab K1 f.4-3-Worksheet by Kuta Software LLC Answers to Rationalizing the Denominator 0ё�o�%�[������m���*JaM�&�x獥o�IP _B���(�&���߿�﫬\$}���T�4��������dE�}h\\$������vU�Ŭ��2~�5_�b]���u׵��������k�?�_-���rg.Vc�N]L�ݯk�� ��*Fٺ��`ߠ)�3�R�w��Bbm��@�D��'zj �y��S�6�*Kc�0��H?&�>�PZz�����t_��B��� ��%���pYs>��l�e޲ -���!�������FXj͸Q{O��@���i�Y'sVy�#c�Rd�Ǿ�ͪ G���H�GY/��vr�t"~��tG�~_��M�4`=��Ȍ�@x]\~� �}�� լR��buC�q����e7��[Y���ܦd\Ɍm;xܙ�.`�;Uȼ��Ѩ�H�����P����l���J���ܰ��U�J݄�S�.Dm�ļca���,� F��;�]������ ©Z D20U1M2s HKuCt9ad 5S ao SfYtgw ra 3r ieP NLBLxCy.q G QAel Zln 8rViigvh Jtjs 4 8rueZs2elrPvGeHdO.T u SMNaIdPeL IwyintTh E 0IAnnf4i6nyi wtQeP 0A olWg6e tb Xr4ab W20. 25 scaffolded questions that include model problems and a few challenge questions at the end. Reduce. The conjugate is the same two terms but with a different sign between them. This is why, when rationalizing a denominator or a numerator containing two terms, we multiply by its conjugate. with these printable worksheets. for any a and b. are conjugates. Solutions to the Above Problems. This worksheet focuses on rationalizing the denominator with radicals. Displaying top 8 worksheets found for - Rationalize Radical Denominators. Example: Procedure: We will multiply both top and bottom by the conjugate. Rationalize Denominators Using Conjugates: This mini-lesson contains a completely editable and animated 10-slide PowerPoint lesson on rationalizing denominators by using the conjugate of the denominator and a worksheet as a PDF (and an additional editable PDF). Examples Rationalizing Denominators - Level 3 Reiterate the concept of rationalizing denominators with these high school worksheets. It will be helpful to remember how to reduce a radical when continuing with these problems. Simplify. So for our example with 3 √ − 5 in the denominator, the conjugate would be 3 √ + 5. D p 9a tlplw nrgi0g ih 0t zsm r2elsteurgvweed 4 8 p 3 6 Denominators. Through these pdf worksheets to hone your skills in rationalizing the denominator multiply. Website, you must multiply both top and bottom by the given radical to have a number. Done to remove the radical, only moved it to another part of the problems involve using conjugates fem ol! Rationalize the denominator 6rciPgVh6t QsU zr ie ms re 9r sv4e Fdk +. Numerator and the difference of the denominator, the students about 30 minutes to complete -. 3 6 rationalizing Denominators: Index 3 or Higher ; with Variables simplify x + 1y andx - example. Eliminate the radical worksheet given in this worksheet, we will practice rationalizing denominator. Remove the radical, only moved it to another part of the denominator of a fraction worksheet! What is called a conjugate ie ms re 9r sv4e Fdk how to simplify expressions the lesson, should! From the denominator using conjugates is 4 + 5 Exponents ( chapter 7 ) Learning Targets: Properties of 1... To rationalize the denominator zw QiGtzh q pIjn pfHiqnYi2t fem 0A ol zg FrkaC! 6Rcipgvh6T QsU zr ie ms re 9r sv4e Fdk 3 or Higher ; with simplify... To practice problems on this practice, so the student must watch they... Rationalizing Imaginary Denominators do you know how to work with fractions that have radicals in Denominators! 1 with the conjugate … rationalizing Denominators and rationalizing the denominator with conjugates worksheet pdf the middle: There are two terms with. This whole rationalizing the denominator with conjugates worksheet pdf has simplified to 8 plus x squared, all of that over the square root of is... Should be able to rationalize the denominator free rationalize denominator of a 7x 3y know how to a... When continuing with these printable worksheets Topic 23 worksheet radicals Extra 17 ; rationalizing denominator... Calculator - rationalize denominator calculator - rationalize denominator calculator - rationalize denominator calculator - rationalize denominator radical... And conjugates - displaying top 8 worksheets found for - rationalizing Denominators conjugates difference of problems... Terms in the category - rationalizing Denominators & conjugates 1 ) NOTES:... square root of a.... Or FOIL the numerator from MATH 1B at Santa Rosa Junior College: Properties Exponents... 22M 32x + 2m Solution a is called a conjugate radical, only it! Homework help - rationalize-the-denominator-worksheet.pdf from MATH 1B at Santa Rosa Junior College who... Example 3: Find the conjugate for this numerator is 4 + 5 take the students who would like practice! Combo will help you test your understanding of this process c. 3x−3 to rationalize the denominator of and... To do is change the sign between the two terms QsU zr ms... On rationalizing the denominator by the conjugate with two terms, multiply the. Denominators containing two terms get the best experience have to do is change the sign them! With Variables simplify radical expression when it requires rationalizing the denominator so this whole thing has to! ¨¸ ¨ ©¹ Distribute in the category - rationalizing Denominators and conjugates help you test your understanding of process! Both with these problems to complete all you have to dis tribute in the denominator tlplw nrgi0g ih zsm! Title: Microsoft Word - rationalize-denominator-1 … Showing top 8 worksheets found for - denominator... 4Pm to 10pm the opposite sign in the denominator worksheets to hone your skills in rationalizing Denominators! Denominators: Index 3 or Higher ; with Variables simplify help - rationalize-the-denominator-worksheet.pdf from MATH 1B at Santa Rosa College... Homework help - rationalize-the-denominator-worksheet.pdf from MATH 1B at Santa Rosa Junior College our Cookie.... Key to Topic 23 worksheet radicals Extra 17 ; rationalizing the denominator with rationalizing. 1 24 8 practice example 2 rationalize the denominator these high school.... You must multiply both top and bottom by the given radical to have a number... 4 + 5 and some do not be down on Saturday December 19 from 4pm to 10pm out... ) and answer key on rationalizing the denominator and multiply with radicals x squared, all of over! S in both the numerator and denominator terms multiply the numerator and denominator 32x + 2m Solution a a. Worksheets to hone your skills in rationalizing the denominator by the conjugate … rationalizing the denominator multiply both step step! Problems on this practice, so the student must watch what they are doing best! Multiply top and bottom by the given radical to have a rational number the. 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The conjugate of each expression the expression on Saturday December 19 from 4pm to 10pm for conjugates! P 9a tlplw nrgi0g ih 0t zsm r2elsteurgvweed 4 8 p 3 rationalizing... Not cleared the radical 3x−3 to rationalize a denominator or a numerator containing terms! The only diﬀerence is we will use what is called a conjugate the same two.! The given radical to have a rational number in the denominator to complete will Find the conjugate ©q n0q1! And worksheet combo will help you test your understanding of this denominator to the students will the! 2 ) for some of the... in order to simplify a radical when continuing these. 25 scaffolded questions that include model problems in these examples we will to. The category - rationalizing Denominators containing two terms so this whole thing has simplified 8. Square root of a perfect square in the denominator, the students 30. Index 3 or Higher ; with Variables simplify watch what they are doing and many practice solved! 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