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- Finds the cube root, fourth root or any nth root of a number.
- Simplifies radicals, such as ∛54 = 3∛2.
- Tells you if the number is a perfect square, cube or power.
- Works with negative numbers for odd roots, such as ∛(−27) = −3.
How to use the root calculator
Enter the number
The radicand, for example 54.
Enter the root index
2 for a square root, 3 for a cube root, 4 for a fourth root and so on.
Pick the decimal places
From 2 to 10.
Read the answer
See the decimal value, the simplified radical and a check.
What is an nth root?
The nth root of x is the number that gives x when multiplied by itself n times. The cube root of 27 is 3, because 3 × 3 × 3 = 27. Odd roots of negative numbers are negative, but even roots of negative numbers are not real numbers.
Root formulas
ⁿ√x = x^(1/n)
ⁿ√(aⁿ × b) = a × ⁿ√b
(ⁿ√x)ⁿ = x
To simplify a radical, pull out the largest perfect nth power factor.
Example 1: cube root of 54
Simplify the radical.
- Largest cube factor 27 × 2
- Simplified 3∛2
- Decimal 3.779763
Example 2: perfect roots
Exact answers.
- ∛27 3
- ∛(−27) −3
- ⁵√32 2
- ∜16 2
Example 3: more roots
Rounded to 6 decimal places.
- ∛2 1.259921
- ∛128 4∛2 ≈ 5.039684
- √72 6√2 ≈ 8.485281
Where roots are used
Algebra
Simplify radicals and solve equations like x³ = 54.
Geometry
Find the side of a cube from its volume.
Finance
Yearly growth rates use nth roots, as in CAGR.
Science
Work with cube roots in physics and chemistry formulas.
For square roots in detail, use the square root calculator. Raise numbers to powers with the exponent calculator, or find growth rates with the CAGR calculator.
Root calculator FAQ
What is the cube root of 27?
3, because 3 × 3 × 3 = 27.
How do you simplify a cube root?
Find the largest perfect cube that divides the number and take it outside. ∛54 = ∛(27 × 2) = 3∛2.
Can you take the cube root of a negative number?
Yes. The cube root of −27 is −3.
Can you take the square root of a negative number?
Not as a real number. Even roots of negative numbers are imaginary.
How do you write an nth root as an exponent?
ⁿ√x = x^(1/n). For example, ∛8 = 8^(1/3) = 2.
What is a perfect cube?
A number that is a whole number cubed, such as 8, 27, 64 and 125.