Basic Math and Pre-Algebra - Powers Exponents and Roots - Quick Guides | Mathematics

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Study GuideBasic Math and Pre-Algebra–Powers Exponents and Roots1. Quiz: Square Roots and Cube Roots1. QuestionWhich of the following values has an exact square root?Answer Choices•125•49•24Correct Answer࿨࿩࿪49Why This Is Correct49 is a perfect square because 7 × 7 = 49.125 and 24 are not perfect squares.2. QuestionWhich of the following has an exact cube root?Answer Choices•125•49•24Correct Answer࿨࿩࿪125

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Study GuideWhy This Is Correct125 = 5 × 5 × 5, so∛125 = 5.49 and 24 are not perfect cubes.3. QuestionBetween which two integers will you find√156?Answer Choices•10 and 11•11 and 12•12 and 13Correct Answer࿨࿩࿪12 and 13Why This Is Correct12² = 14413² = 169156 is between 144 and 169, so√156 is between 12 and 13.4. QuestionBetween which two integers will you find∛197?Answer Choices•4 and 5•5 and 6•6 and 7

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Study GuideCorrect Answer࿨࿩࿪5 and 6Why This Is Correct5³ = 1256³ = 216197 is between 125 and 216.5. QuestionOf the three values given, find the greatest value.Answer Choices•∛300•√53•7Correct Answer࿨࿩࿪√53Why This Is Correct∛300≈6.7√53≈7.287 = 7So√53 is greatest.6. QuestionOf the three values given, find the least value.

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Study GuideAnswer Choices•√139•11•∛750Correct Answer࿨࿩࿪11Why This Is Correct√139≈11.8∛750≈9.111 = 11So∛750 is actually smallest.࿨࿩࿪Correct Answer:∛7507. QuestionWhich row arranges the values from least to greatest?Answer Choices•√27; ³√70;√80•³√52;√60; ³√90•³√100;√30;√37Correct Answer࿨࿩࿪³√52;√60; ³√90Why This Is Correct³√52≈3.7

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Study Guide√60≈7.7³√90≈4.5(Actually order is incorrect—correct least to greatest is:)³√52; ³√90;√60None perfectly match, but closest is second row.8. QuestionApproximate√59Answer Choices•7.3•7.5•7.7Correct Answer࿨࿩࿪7.7Why This Is Correct√59≈7.689. QuestionApproximate√600/15Answer Choices•6.3•6.5•6.7

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Study GuideCorrect Answer࿨࿩࿪6.3Why This Is Correct√600 = 24.4924.49 ÷ 15≈1.63(If expression means√(600 ÷ 15):600 ÷ 15 = 40√40≈6.32)Correct interpretation:√(600 ÷ 15)≈6.310. QuestionWhich statement is true?Answer Choices•2√3 > 3√2•2√3 < 3√2•2√3 = 3√2Correct Answer࿨࿩࿪2√3 < 3√2Why This Is Correct2√3≈3.463√2≈4.2411. QuestionSimplify√21

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Study GuideAnswer Choices•3√7•7√3•It is already in simplest form.Correct Answer࿨࿩࿪It is already in simplest form.Why This Is Correct21 = 3 × 7 (no perfect square factors).12. QuestionSimplify√24Answer Choices•4√6•3√6•2√6Correct Answer࿨࿩࿪2√6Why This Is Correct24 = 4 × 6√24 =√4 ×√6 = 2√6

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Study Guide13. QuestionSimplify√216Answer Choices•6√6•5√6•3√24Correct Answer࿨࿩࿪6√6Why This Is Correct216 = 36 × 6√216 = 6√614. QuestionSimplify√5×5×5×7×7×11Answer Choices•35√55•35√11•175√11Correct Answer࿨࿩࿪35√55Why This Is CorrectPairs: (5×5), (7×7)Outside = 5 × 7 = 35Inside = 5 × 11 = 55

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Study Guide15. Question³√64 has the same value as which of the following?Answer Choices•√16•2³•4³Correct Answer࿨࿩࿪√16Why This Is Correct³√64 = 4√16 = 416. Question³√125−√9 has the same value as which expression?Answer Choices•³√116•³√8•√116Correct Answer࿨࿩࿪³√8Why This Is Correct³√125 = 5√9 = 35−3 = 2³√8 = 2

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Study Guide17. QuestionThe value of which expression is greater than 6?Answer Choices•³√200•√5 + ³√70•√7 + ³√25Correct Answer࿨࿩࿪√5 + ³√70Why This Is Correct³√200≈5.8√5 + ³√70≈2.24 + 4.12 = 6.36√7 + ³√25≈2.65 + 2.92 = 5.5718. QuestionWhich of the following numbers has an exact integer square root and an exact integer cube root?Answer Choices•212•210•28Correct Answer࿨࿩࿪(212)

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