The square root of n is the non-negative number that squares to n.
About this calculator
The square root of n is the non-negative number that squares to n. Enter 144 and you get 12 exactly. Enter 50 and you get about 7.071 plus the simplified form 5√2.
Perfect squares — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 — have integer roots. For everything else the decimal keeps going; simplified radical form is often what teachers want on paper.
Pair with the [[square]] calculator to check n², the [[simplify-radicals]] tool to factor the radicand, and the [[root]] calculator for nth roots. For side lengths from areas use [[pythagorean]].
Common uses
- Find √144 or other perfect squares for homework
- Convert area to side length for a square plot
- Check whether a number is a perfect square
- Get simplified radical form like 2√18 → 6√2
- Estimate square roots between known perfect squares
Frequently asked questions
What is the square root of 144?
√144 = 12 exactly because 12 × 12 = 144. The simplified form is also just 12 with no radical left inside.
Can you take the square root of a negative number?
Not in the real number system. √−4 has no real answer. Complex numbers extend this, but this calculator stays with real results.
What is simplified radical form?
Pull out the largest perfect-square factor. √50 = √(25 × 2) = 5√2. The number under the radical should have no perfect-square factors left.
How is square root related to exponents?
√n equals n raised to the 1/2 power. So √144 = 144^(1/2) = 12. See the [[fractional-exponents]] calculator for more.