Square Root Calculator

Calculate the square root (√) of any positive number instantly with our free online Square Root Calculator. Ideal for students, engineers, scientists, builders, programmers and anyone working with mathematics.

✔ Square roots • ✔ Decimal precision • ✔ Instant calculation • ✔ Free calculator

What is a Square Root Calculator?

A Square Root Calculator finds the number that, when multiplied by itself, equals the original number. Square roots are fundamental in mathematics and are widely used in algebra, geometry, engineering, physics, statistics, finance and computer science.

Simply enter any positive number and the calculator instantly determines its square root, verifies the result and identifies whether the number is a perfect square.

What is a Square Root?

The square root of a number is the value that, when multiplied by itself, produces the original number.

For example:

• √16 = 4 because 4 × 4 = 16
• √81 = 9 because 9 × 9 = 81
• √225 = 15 because 15 × 15 = 225

Perfect Squares

A perfect square is a number whose square root is a whole number.

Common Square Roots

Number	Square Root
1	1
4	2
9	3
16	4
25	5
36	6
49	7
64	8
81	9
100	10
121	11
144	12
169	13
196	14
225	15

Worked Examples

Example 1 — √16

• Input = 16
• Square Root = 4
• Verification: 4 × 4 = 16
• Perfect Square = Yes

Example 2 — √144

• Input = 144
• Square Root = 12
• Verification: 12 × 12 = 144
• Perfect Square = Yes

Example 3 — √2

• Input = 2
• Square Root ≈ 1.414214
• Perfect Square = No

Where are Square Roots Used?

Square Roots in Geometry

Square roots are essential when applying Pythagoras' Theorem.

This allows the length of the hypotenuse of a right-angled triangle to be calculated accurately.

Things to Remember

• Square roots are the opposite of squaring.
• Every positive number has one positive square root.
• Perfect squares have whole-number square roots.
• Many square roots are irrational numbers with infinitely many decimal places.
• Negative numbers do not have real square roots.

Frequently Asked Questions

What is √16?

√16 = 4.

What is √100?

√100 = 10.

Can square roots be decimals?

Yes. Most numbers are not perfect squares and therefore have decimal square roots.

Can this calculator handle large numbers?

Yes. It calculates square roots for both small and very large positive numbers instantly.

Why are square roots important?

Square roots are used throughout mathematics, engineering, science, finance, architecture and computer graphics.

✔ Free • ✔ Fast • ✔ No signup required • ✔ No DATA collected

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