Radicals and rational exponents

Simplifying square and cube roots, and the same numbers written as fractional powers.

4 sheets · 40 questions · one answer key · 5 pages

Recommended for grades 10–11

Save as PDF Customize

Square roots Sheet 1 of 4

Simplifying radicalsSquare roots

Name: Date:

Simplify each square root.

1162

2375

3396

4810

5200

660

7343

8300

9640

10108

Simplifying radicalsCube roots

Name: Date:

Simplify each cube root.

1135

254

3270

432

5128

6750

7640

8704

9448

10297

Rational exponentsRoots only

Name: Date:

Work out each one. The bottom number says which root to take.

11001/2 =

25121/3 =

341/2 =

41251/3 =

524011/4 =

66251/4 =

7100001/4 =

87291/3 =

9641/2 =

10491/2 =

Rational exponentsRoots and powers

Name: Date:

Work out each one. Take the root first, then raise it.

11003/2 =

25124/3 =

312965/4 =

43434/3 =

5163/2 =

695/2 =

765613/4 =

840963/4 =

9275/3 =

105122/3 =

Power Pack · Radicals and rational exponentsAnswer key

Square roots

1. √162 = 9√22. √375 = 5√153. √396 = 6√114. √810 = 9√105. √200 = 10√26. √60 = 2√157. √343 = 7√78. √300 = 10√39. √640 = 8√1010. √108 = 6√3

Cube roots

1. ∛135 = 3∛52. ∛54 = 3∛23. ∛270 = 3∛104. ∛32 = 2∛45. ∛128 = 4∛26. ∛750 = 5∛67. ∛640 = 4∛108. ∛704 = 4∛119. ∛448 = 4∛710. ∛297 = 3∛11

Roots as powers

1. 100^(1/2) = 102. 512^(1/3) = 83. 4^(1/2) = 24. 125^(1/3) = 55. 2401^(1/4) = 76. 625^(1/4) = 57. 10000^(1/4) = 108. 729^(1/3) = 99. 64^(1/2) = 810. 49^(1/2) = 7

Roots and powers

1. 100^(3/2) = 10002. 512^(4/3) = 40963. 1296^(5/4) = 77764. 343^(4/3) = 24015. 16^(3/2) = 646. 9^(5/2) = 2437. 6561^(3/4) = 7298. 4096^(3/4) = 5129. 27^(5/3) = 24310. 512^(2/3) = 64

Radicals and rational exponents

What is in the pack

The algebra track

More Algebra 2 packs