Practice Cube Roots in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The cube root x3 is the number that, when cubed, gives x — defined for all real numbers, including negatives.

273 asks: what number times itself times itself equals 27? Answer: 3, because 3×3×3=27. For negatives, −83=−2 because (−2)×(−2)×(−2)=−8.

Showing a random 20 of 50 problems.

Example 1

medium
Simplify 543.

Example 2

hard
Find 0.0083.

Example 3

challenge
A cube of edge a has the same volume as a rectangular box of dimensions 2×4×27. Find a.

Example 4

medium
Simplify 125x6y33.

Example 5

medium
Simplify 543.

Example 6

medium
Is 203 rational or irrational?

Example 7

medium
Between which two consecutive integers does 1003 lie?

Example 8

hard
Solve x3+8=0.

Example 9

medium
Solve x3=−125.

Example 10

easy
Find 10003.

Example 11

medium
Simplify x93 for x>0.

Example 12

easy
What is the cube root of 0?

Example 13

medium
A cube has volume 125 cm3. Find its edge length.

Example 14

easy
Find 643.

Example 15

medium
Find 273⋅83.

Example 16

easy
Find −273.

Example 17

easy
Evaluate −2163.

Example 18

easy
Evaluate 5123.

Example 19

easy
Evaluate −1253.

Example 20

challenge
Simplify 163+543.