What is the square root of a negative number?

There is no real number solution, since a negative number times itself always produces a positive result. The square root of a negative number is an imaginary number, expressed using i.

Why are most square roots long, non-repeating decimals?

Only perfect squares like 4, 9, 16, and 25 have whole-number square roots. Every other positive number has an irrational square root with an infinite, non-repeating decimal expansion.

Where are square roots used outside of math homework?

The Pythagorean theorem, standard deviation calculations in statistics, and various physics formulas involving distance and energy all rely on square roots.

Square Root Calculator

Calculate square roots, cube roots, nth roots, squares, cubes, and powers with precision.

Number

Decimal places

Nth root (n)

Power & Exponent Calculator

Base (n)

Exponent

Common Square Roots (1–20)

How to use

Enter a number in the top field and click Calculate to see its square root, cube root, and nth root.
Set the Nth root field to any value — for example, 4 gives you the 4th root (⁴√n).
Adjust Decimal places to control the precision of results (2–10 places).
Use the Power Calculator to compute n² (square), n³ (cube), or any base raised to an exponent.
The common square roots table below shows √1 through √20 for quick reference.
A Perfect Square badge tells you whether the number is a whole-number square.

About this Square Root Calculator

The square root of a number is the value that, multiplied by itself, produces that number. The square root of 25 is 5, because 5 × 5 = 25. Most square roots outside of perfect squares (1, 4, 9, 16, 25...) are irrational numbers with infinite non-repeating decimals, which is why a calculator is far faster than manual estimation for most values.

Perfect squares worth memorizing

1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49, 8²=64, 9²=81, 10²=100, 11²=121, 12²=144. Recognizing these makes it easy to estimate square roots of nearby numbers — the square root of 130 must be just above 11 (since 11²=121) and below 12 (since 12²=144).

Negative numbers and square roots

No real number multiplied by itself produces a negative result (a negative times a negative is positive, and a positive times a positive is also positive). The square root of a negative number is an imaginary number, expressed using i (where i² = −1) — a concept from higher-level algebra, not something a standard calculator resolves to a real decimal value.

Where square roots show up outside math class

The Pythagorean theorem (finding the diagonal of a rectangle or the hypotenuse of a right triangle) requires a square root. Standard deviation in statistics is defined as the square root of variance. Physics formulas involving distance, velocity, and energy frequently involve square roots as well.