Square Root Calculator
Find the square root of any number, simplify a radical to aโb form, and calculate cube roots and nth roots. Shows exact simplified surds where possible.
Result
8.485281374
โ72
Simplified radical form
6โ2
Radical simplification factors out the largest perfect square, e.g. โ72 = 6โ2. Odd nth roots of negative numbers return the real root; even roots of negatives are imaginary.
Frequently Asked Questions
How do I simplify a square root?
Factor out the largest perfect square. โ72 = โ(36 ร 2) = 6โ2. This calculator finds the largest perfect-square factor automatically and shows the result in aโb form, where b has no remaining square factors.
What is the square root of a negative number?
There is no real square root of a negative number, because no real number squared is negative. The result is an imaginary number โ for example, โ(โ9) = 3i, where i is the square root of โ1.
How do I find a cube root or an nth root?
An nth root asks what number, raised to the n, equals your value. The cube root of 27 is 3 because 3ยณ = 27. This calculator computes any nth root; for negative inputs it returns the real root when n is odd.
What is a perfect square?
A perfect square is a whole number that is the square of an integer: 1, 4, 9, 16, 25, 36, and so on. The square root of a perfect square is a whole number, so it simplifies to an exact value with no radical left.
Is the square root always positive?
Every positive number has two square roots, one positive and one negative, because both (+x)ยฒ and (โx)ยฒ give the same value. By convention the radical symbol โ means the principal (non-negative) root, which is what this calculator reports.