Square Root Calculator

Written byOleh Soloninupdated 5 October 2026

Number under the root

Root degree

2 for a square root, 3 for a cube root.

Result

Root5.656854
Simplified√32 = 4√2
Check5.65685425² ≈ 32

The number that multiplies by itself to reach yours

Find the square root of any positive number, with enough decimal places for geometry, construction and physics work.

A square root answers a geometric question: given an area, how long is the side of the square? The area 144 gives a side of 12.

Most roots are irrational — they run forever without repeating. √2 starts 1.41421356 and never settles, which is exactly what unsettled the ancient Greeks about it.

How to use

Enter the number under the root.
Choose the degree: 2 for a square root, 3 for a cube root, and so on.
Read the decimal value, the simplified radical form and the check that squares the answer back.

Exact form and decimal form

Most roots are irrational, so a decimal is always an approximation. The exact form keeps the root intact and pulls out whatever perfect square hides inside: √32 becomes 4√2, and √1,000 becomes 10√10. Nothing is lost in that rewriting, which is why textbooks prefer it.

A root is also a fractional power, and that is how calculators reach it: √32 is 32^0.5. It makes cube and higher roots no harder — a cube root is the power of one third.

Worked out with this calculator.
Root	Decimal	Simplified
√144	12	12, exact
√32	5.6569	4√2
√1,000	31.6228	10√10
√2	1.4142	cannot be simplified

What this calculator shows

The square root to several decimal places
Instant identification of perfect squares
Precision suitable for diagonals, distances and areas

What to keep in mind

Returns the positive root. Strictly, 9 has roots of both 3 and −3.
Negative inputs have no real square root; they belong to the imaginary numbers.

FAQs

What is the square root of 144?

12, because 12 × 12 = 144. It is a perfect square, so the answer is a whole number.

Why can't I take the square root of a negative number?

Because any real number times itself is positive or, for zero, zero — never negative. Mathematics gets around it by inventing i, where i² = −1, but that leaves the real number line.

How would I estimate √50 without a calculator?

It sits between √49 = 7 and √64 = 8, much closer to 7. To two decimals it is 7.07; exactly, 5√2.

What is a perfect square?

A number whose root is a whole number: 1, 4, 9, 16, 25, 36 and so on. Every whole number between them has an irrational root; a fraction such as 2.25 can still have a rational one, 1.5.

What is the square root of 32?

About 5.6569, and exactly 4√2. The largest perfect square inside 32 is 16, and pulling it out leaves 4 outside the root and 2 inside.

When can a root be simplified?

When the number contains a perfect square factor. 32 contains 16 and 1,000 contains 100, so both simplify; 2 contains neither and stays as it is.

Worked example

The diagonal of a square room

Input: √32

Output: 5.657

Note: A room 4 m by 4 m has a diagonal of √(16+16) = √32, about 5.66 m — worth knowing before carrying a sofa through it.

Useful links

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Square Root Calculator

Result

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