Cube Root Calculator
Type a number to get its cube root, see whether it is a perfect cube and get the simplest form from its prime factors.
- Nothing you type is stored
- Free
- No signup
Root
3.7797631497
- Written as
- ∛54
- Simplest surd form
- 3∛2
- Check
- 3.7797631³ ≈ 53.99999787
Show working
- 54 = 2 × 3³
- ∛54 = ∛(3³ × 2) = 3∛2
- = 3 × 1.25992105 = 3.77976315
How to use
- Keep Cube ∛ selected.
- Type the number (negative numbers are fine).
- Read the cube root, the simplest form and the steps.
Good to know
The cube root of x is the number that gives x when multiplied by itself three times: ∛125 = 5 because 5 × 5 × 5 = 125. Unlike square roots, negative numbers have a real cube root: ∛−27 = −3.
To simplify, group equal prime factors in threes: 54 = 2 × 3³, so ∛54 = 3∛2. A number is a perfect cube when every exponent in its prime factorisation is a multiple of 3, such as 1,728 = 2⁶ × 3³ = 12³. NCERT Class 8 covers this in 'Cubes and Cube Roots'.
Cube roots appear in volume problems: a cube-shaped tank holding 8,000 litres (8 m³) has sides of ∛8 = 2 m. Remember perfect cubes up to 20³ = 8,000; they make estimates quick.
Questions
What is the cube root of 1000?
10, because 10 × 10 × 10 = 1000.
Can a negative number have a cube root?
Yes. A negative times a negative times a negative is negative, so ∛−64 = −4.
How do I find a cube root by prime factorisation?
Write the number as prime factors, group them in threes and take one factor from each group. 3375 = 3³ × 5³, so ∛3375 = 3 × 5 = 15.
What is the cube root of 2?
About 1.2599210499. It is irrational.
How is a cube root different from dividing by 3?
Completely: ∛27 = 3, but 27 ÷ 3 = 9. The cube root undoes cubing, not tripling.