University:
Cornell University
Course:
MATH 1101 | Calculus Preparation
Academic year:

2020
Views:

319

Pages:

2
Author:

StellarSymphony

Algebra 2 Honors Radicals Quiz Review Name________________ Date_________________ Simplify. Assume that the given radicals denote real numbers. You may not leave radicals in the denominator, or negative exponents in your final answer. 1. √12𝑥 5 2. 4. √2𝑥 −3 ∙ √6𝑥 5. 7. √9𝑎2 − 9𝑏 2 8. 3 8𝑐 √ 3 3 √6𝑐 ∙ √8𝑐 −5 6. √3𝑥 2 − 12𝑥 + 12 9. Simplify. Assume that the given radicals denote real numbers. 10. 𝑦 2 √45𝑦 + 2𝑦√5𝑦 3 13. √6𝑥 + √2𝑥 √3 3𝑥 −√2 3 √32𝑎−3 𝑏 4 3. 9𝑑5 √27𝑥 √3𝑥 −1 3 3 √−16𝑥 3 𝑦 4 𝑧 ∙ √−2𝑧 5 3 3 √320+ √1250 11. √2𝑎2 𝑏 4 + √8𝑎2 𝑏 4 12. 14. √10𝑡(√2𝑡 5 − √5𝑡) 15. √8 (√4 + 3 2 √5 3 3 2 ) √3 Simplify using Rational Exponents. Assume that the given radicals denote real numbers. You may not leave radicals in the denominator, or negative exponents in your final answer. Please keep your final answers in Radical Form. 17. (√8𝑥 3 𝑦 −9 ) 6 6 3 18. √273 5 √92 3 4 5 1 21. (𝑥 2 − 2𝑥 2 ) ÷ 𝑥 2 20. √83 ÷ √42 19. √8 ∙ √16−1 4 5 3 3 16. 25−2 3 22. ( √ 3√81) ÷ √√27 Simplify. Assume that the given radicals denote real numbers. You may not leave radicals in the denominator, or negative exponents in your final answer. 2 23. 7𝑎−√𝑏 ∙ 7𝑎+√𝑏 24. 254+3√5 ÷ (1251+√5 ) Find the roots of each equation. 25. 4 − 16𝑥 2 = 0 26. 25𝑦 2 + 16 = 17 27. 2𝑥 5 + 73 = 53 3 3 28. Prove that if a and b are rational numbers, (𝑎 + √𝑏) + (𝑎 − √𝑏) is also rational. 29. A right triangle has side lengths 𝑥 + 3 and 1, and hypotenuse 𝑥 + 5. Find the value of x and the length of each side. Answers 3 1. 2𝑥 2 √3𝑥 2. 6. 3|𝑥| 7. 11. 3|𝑎|𝑏 2 √2 15. 7√2 8 3. 3𝑑2 3√𝑎2 − 𝑏 2 12. 2 + 16. 3 2 √3𝑐𝑑 3 5 √2 2 1 1 25. 𝑥 = ± 2 13. 17. 125 21. 𝑥 − 2𝑥 2 20. √2 8. 1 26. 𝑥 = ± 5 2𝑏 √4𝑏 3 2 √6𝑐 2 4. 2√3 |𝑥| 5. |𝑥 − 2|√3 9. 2𝑥𝑦𝑧 2 3√4𝑦 10. 5𝑦 2 √5𝑦 5√6𝑥 14. 2|𝑡 3 |√5 − 5|𝑡|√2 𝑎 6 16𝑥 4 √2𝑥𝑦 𝑦 14 22. √3 𝑐2 6 18. 3 19. √32 23. 72𝑎 24. 25 5 27. 𝑥 = − √10 28. 2𝑎3 + 6𝑎𝑏, All Rational Numbers and Rationals are closed under addition and multiplication! 29. Not Possible!