Square Root Calculator
Square, cube and nth roots with simplest radical form.
About this tool
Enter a number and the root (2 for square root, 3 for cube root, and so on). The tool gives the decimal value, the simplest radical form for integers, whether it's a perfect power, the nearest perfect squares, and a check by raising the answer back to the power.
Roots and radicals
The square root of x is the number whose square is x: √144 = 12. Most whole numbers aren't perfect squares, so their roots are irrational decimals that never end (√2 = 1.414213562373095…). In algebra the convention is to leave them in simplest radical form by taking out every square factor: √72 = √(36 × 2) = 6√2, and √50 = 5√2. The same works for cube roots (∛54 = ∛(27 × 2) = 3∛2) and higher roots. The tool finds these automatically, says whether the number is a perfect square, cube or higher power, and lists the nearest perfect squares either side, handy for estimating, since √72 lies between 8 (√64) and 9 (√81). For very large integers it also computes the exact integer square root with arbitrary precision. Odd roots of negative numbers are real and negative (∛−8 = −2); even roots of negative numbers are imaginary (√−9 = 3i). Honest limits: decimals are rounded floating-point values, and radical simplification works for integers up to 10¹⁵. The exponent calculator and the Pythagorean theorem calculator are related.
Frequently asked questions
How do I simplify a square root?
Factor out the largest perfect square: √72 = √(36 × 2) = 6√2.
What is the square root of 2?
About 1.414213562373095. It is irrational, so the decimal never ends or repeats.
Can you take the square root of a negative number?
Not as a real number. √−9 = 3i, using the imaginary unit i.
What is a perfect square?
A whole number that is another whole number squared, like 49 = 7².
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.