How this calculator works
The principal square root is the non-negative number that gives the input when multiplied by itself. A perfect square has an integer square root. Other inputs often have irrational roots, so the displayed decimal is an approximation. This calculator works with real numbers and rejects negative inputs.
Formula
r = √x, with r ≥ 0 and r² = x. Domain: x ≥ 0.
Worked example
The square root of 144 is 12 because 12 × 12 = 144. The square root of 2 is approximately 1.41421356, while the square root of zero is zero.
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Frequently asked questions
Why is the answer not both positive and negative?
The symbol √ denotes the principal, non-negative root. The equation y² = 144 has two solutions, 12 and -12, but √144 is 12.
Can I calculate the square root of a negative number?
A negative number has no real square root. Complex roots require the imaginary unit i and are outside this calculator.
Does this calculate cube roots?
No. The page finds only the principal square root. A cube root is a different operation and can also accept negative numbers.