Practice Cube Roots in Math

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

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Quick Recap

The cube root x3\sqrt[3]{x} is the number that, when cubed, gives xx — defined for all real numbers, including negatives.

273\sqrt[3]{27} asks: what number times itself times itself equals 27? Answer: 3, because 3×3×3=273 \times 3 \times 3 = 27. For negatives, −83=−2\sqrt[3]{-8} = -2 because (−2)×(−2)×(−2)=−8(-2) \times (-2) \times (-2) = -8.

Showing a random 20 of 50 problems.

Example 1

medium
Simplify 543\sqrt[3]{54}.

Example 2

hard
Find 0.0083\sqrt[3]{0.008}.

Example 3

challenge
A cube of edge aa has the same volume as a rectangular box of dimensions 2×4×272 \times 4 \times 27. Find aa.

Example 4

medium
Simplify 125x6y33\sqrt[3]{125x^6 y^3}.

Example 5

medium
Simplify 543\sqrt[3]{54}.

Example 6

medium
Is 203\sqrt[3]{20} rational or irrational?

Example 7

medium
Between which two consecutive integers does 1003\sqrt[3]{100} lie?

Example 8

hard
Solve x3+8=0x^3 + 8 = 0.

Example 9

medium
Solve x3=−125x^3 = -125.

Example 10

easy
Find 10003\sqrt[3]{1000}.

Example 11

medium
Simplify x93\sqrt[3]{x^9} for x>0x > 0.

Example 12

easy
What is the cube root of 00?

Example 13

medium
A cube has volume 125 cm3125\,\text{cm}^3. Find its edge length.

Example 14

easy
Find 643\sqrt[3]{64}.

Example 15

medium
Find 273⋅83\sqrt[3]{27}\cdot\sqrt[3]{8}.

Example 16

easy
Find −273\sqrt[3]{-27}.

Example 17

easy
Evaluate −2163\sqrt[3]{-216}.

Example 18

easy
Evaluate 5123\sqrt[3]{512}.

Example 19

easy
Evaluate −1253\sqrt[3]{-125}.

Example 20

challenge
Simplify 163+543\sqrt[3]{16}+\sqrt[3]{54}.
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