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What is the Square Root of 500?

The square root of 500 is 22.360679775. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√500 = 22.360679775
CalculatedNon-perfect squareIrrational
Exact form√500
Perfect squareNo
Number typeIrrational
Verification22.3606797752 ≈ 500

On this page

How the answer is calculated

We solve x2 = 500. The resulting value is x = 22.360679775.

Verification: 22.3606797752 ≈ 500.

Simplified radical form

The square root of 500 in simplified radical form is 10√5.

This is equivalent to √500, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal22484
Upper or equal23529

Nearby square roots

NumberSquare root
√49722.2934968096
√49822.3159136044
√49922.3383079037
√50022.360679775
√50122.3830292856
√50222.4053565024
√50322.427661492

Number properties

Is 500 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√500 is irrational because 500 is not a perfect square.

Visual guide

Square Root function graph

See how the result changes as the input moves across positive and negative values. Square roots are shown for non-negative inputs; cube roots continue through negative inputs.

Common questions

Frequently asked questions

It asks for the number that, when raised to the power of 2, equals 500.