Root Calculator guide
Root Calculator: Square Roots, Cube Roots and Surds
Use our root calculator to find square roots, cube roots and nth roots of any number, and to simplify square roots into surds.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
A root is the opposite of a power. The square root of 25 is 5, because 5² = 25. Our Root Calculator works out any root and simplifies surds.
How to use the calculator (Root Calculator)
- Enter the number.
- Enter the root: 2 for a square root, 3 for a cube root and so on.
You'll see the answer, plus the square, cube, fourth and fifth roots side by side.
How roots work
The nth root of x is the number that gives x when multiplied by itself n times:
ⁿ√x = x^(1/n)
- Square root: √36 = 6, because 6 × 6 = 36
- Cube root: ∛27 = 3, because 3 × 3 × 3 = 27
Simplifying surds
A surd is a root that isn't a whole number. You can simplify it by taking out square factors:
√72 = √(36 × 2) = 6√2
A worked example
With the calculator's default settings, √72 is about 8.485, which simplifies to 6√2.
Frequently asked questions
Can I find the square root of a negative number?
Not as a real number. Even roots of negative numbers are imaginary. Odd roots work fine: ∛−27 = −3.
What are perfect squares?
Numbers whose square root is a whole number: 1, 4, 9, 16, 25, 36 and so on.
How do I estimate a square root?
Find the perfect squares either side. √50 is between √49 = 7 and √64 = 8, so it's just over 7.
For powers, use our Exponent Calculator.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Square rootmathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.