√ Square Root Calculator

What This Calculator Does

This calculator finds the square root of any number you enter — the value that, multiplied by itself, gives your number. The square root of 25 is 5, because 5 times 5 is 25. For numbers that are not perfect squares, it returns a precise decimal, so you get an accurate answer whether your number is a clean square or not.

Square roots come up far more often than most people expect — in geometry, in statistics, in physics, and in everyday measurement problems. Having an instant, accurate calculator means you never have to estimate or reach for a clunkier tool.

Understanding Square Roots

A square root undoes squaring. Squaring a number means multiplying it by itself; the square root reverses that, asking “what number, squared, gives this?” Perfect squares like 4, 9, 16, and 25 have whole-number roots (2, 3, 4, and 5). Most numbers do not — the square root of 2, for instance, is an endless, non-repeating decimal beginning 1.414, which is why a calculator is the practical way to find it.

Every positive number technically has two square roots, one positive and one negative, since a negative times a negative is also positive. By convention the “principal” square root is the positive one, which is what this calculator returns. Negative numbers have no real square root at all, because nothing real, squared, gives a negative result — that territory belongs to imaginary numbers.

Estimating Square Roots in Your Head

You can often approximate a square root without any tool by anchoring on nearby perfect squares. To estimate the square root of 50, note that 7 squared is 49 and 8 squared is 64. Since 50 is just above 49, its square root is just above 7 — about 7.07. This bracketing technique gets you a quick, reasonable estimate, which is handy as a sanity check on a calculated answer.

For a closer estimate, judge how far your number sits between the two perfect squares and nudge accordingly. The skill is useful not because you will replace the calculator, but because a rough mental figure tells you immediately whether a precise answer looks right — a good habit that catches input errors before they cause problems.

Frequently Asked Questions

What is a square root?

It is the number that, multiplied by itself, gives your original number. The square root of 36 is 6, because 6 × 6 = 36. This calculator finds it for any number, including those without whole-number roots.

Why do some square roots have endless decimals?

Because the number is not a perfect square. The square root of 2, for example, is irrational — its decimal goes on forever without repeating. The calculator gives a precise decimal approximation to as many places as you need.

Can you take the square root of a negative number?

Not within the real numbers, because no real number squared gives a negative result. Negative numbers have “imaginary” square roots, a concept used in advanced math but outside what this calculator handles.

Does every number have two square roots?

Every positive number has two — one positive and one negative — since both squared give the same positive result. By convention the principal square root is the positive value, which is what this tool returns.