Square Root Calculator

By convention, the symbol √ means the principal square root, which is the positive one. It is true that both 12 and −12 square to give 144, and equations like x² = 144 have both solutions — but √144 itself is defined as 12. If you need both solutions of an equation, take the calculator's answer and use it with both signs.

Find the largest perfect square that divides the number — for 72 that is 36 — and write the number as 36 × 2. The square root of 36 is exactly 6, which moves outside the root sign, leaving √72 = 6√2. If no perfect square larger than 1 divides the number (as with √7 or √13), the surd is already in its simplest form.

Not within real numbers. Squaring any real number — positive or negative — gives a positive result, so no real number squares to −9. Mathematicians handle these with imaginary numbers (√−9 = 3i), which this calculator does not cover; entering a negative number gives an explanation instead of a wrong answer.

Yes. √2 ≈ 1.41421356… is irrational: its decimal expansion never ends and never repeats a pattern, so any decimal answer is a rounded approximation. That is why the calculator also shows the exact surd form where it can (for example 6√2) — the surd is exact, the decimal is rounded to the places shown.

Bracket it between two perfect squares. √50 lies between √49 = 7 and √64 = 8, and since 50 is very close to 49, the answer is just above 7 (the true value is about 7.07). This bracketing is also a good sanity check on any calculator result.

No. It runs 100% in your browser — the number you enter is rooted locally on your device, nothing is uploaded or stored, and there is no record of your calculation once you close the page.