Square Root Calculator

Use this square root calculator to find the square root of a number instantly. Enter any positive number to see the square root, a squared check and whether the number is a perfect square.

This calculator is useful for maths homework, quick checks, number practice and everyday calculations.

What is a square root?

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

For example:

• the square root of 9 is 3
• because 3 × 3 = 9

The square root symbol is √.

Square root formula

The square root of a number x is written as:

√x

For example:

√16 = 4

because:

4 × 4 = 16

How to use this square root calculator

1. Enter a number in the input box.
2. The calculator updates instantly.
3. You will see:
   • the square root
   • the squared check
   • whether the number is a perfect square

Use the Reset button to clear the field and start again.

Examples of square roots

Example 1: Perfect square

√25 = 5

because:

5 × 5 = 25

Example 2: Another perfect square

√144 = 12

because:

12 × 12 = 144

Example 3: Non-perfect square

√20 ≈ 4.472136

because:

4.472136 × 4.472136 ≈ 20

Perfect squares

A perfect square is a number that has a whole-number square root.

Examples of perfect squares include:

• 1
• 4
• 9
• 16
• 25
• 36
• 49
• 64
• 81
• 100

For example, 49 is a perfect square because √49 = 7.

What if the number is not a perfect square?

If a number is not a perfect square, its square root will be a decimal.

For example:

• √2 ≈ 1.414214
• √10 ≈ 3.162278
• √50 ≈ 7.071068

This calculator rounds the result for easy reading.

Can you find the square root of a negative number?

In standard real-number maths, negative numbers do not have a real square root.

For example, √-9 is not a real number.

This calculator is designed for real square roots only, so it accepts 0 and positive numbers.

Why square roots are useful

Square roots appear in many areas of maths and everyday problem-solving, including:

• geometry
• algebra
• trigonometry
• statistics
• science and engineering
• area and distance calculations

They are especially common when working backwards from squared values.

Frequently asked questions

How do you calculate a square root?

A square root is a number that multiplies by itself to give the original number. For exact answers, some numbers have whole-number roots, while others produce decimals.

What is the square root of 64?

The square root of 64 is 8, because 8 × 8 = 64.

What is a perfect square?

A perfect square is a number with a whole-number square root, such as 9, 16 or 100.

Can a square root be a decimal?

Yes. If the number is not a perfect square, the square root will usually be a decimal.

Can you square a square root?

Yes. Squaring a square root returns the original number, subject to rounding where decimals are involved.

Why does this calculator reject negative numbers?

This calculator works with real numbers only. Negative numbers require complex numbers, which are outside the scope of this tool.

Check out our other calculators:
Fraction to Decimal