Cube Root Calculator

The cube root of a number is the value that gives that number when multiplied by itself three times. This cube root calculator simplifies cube roots exactly by taking out groups of three equal prime factors, and also gives the decimal. Negative numbers have real cube roots, which are negative.

Try:

How to use the cube root calculator

  1. Enter a number, such as 27, 54 or −64.
  2. Press Calculate.
  3. Read the simplified cube root, the decimal and the steps.

Formula

a3b3=ab3\sqrt[3]{a^3 b} = a\sqrt[3]{b}

Worked example: ∛27

  • Number: 27

✓ Answer checked

33
Step-by-step working (2 steps)

  1. Find the prime factors Prime factorisation

    Break the number into prime factors.

    27=3327 = 3^{3}

  2. Group factors in threes ∛(a³b) = a∛b

    Each group of three equal factors comes out of the root as one factor.

    273=3\sqrt[3]{27} = 3
Formulas used
a3b3=ab3\sqrt[3]{a^3 b} = a\sqrt[3]{b}
How this was checked
  • ✓ Cubing the answer: 3³ × 1 = 27.
  • ✓ Decimal check: (3)³ ≈ 27.

Frequently asked questions

What is the cube root of 27?

3, because 3 × 3 × 3 = 27.

Can a cube root be negative?

Yes. A negative number cubed is negative, so the cube root of −64 is −4.

How do I simplify a cube root?

Prime factorise the number and take out each group of three equal factors. 54 = 2 × 3³, so ∛54 = 3∛2.

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