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What is the Square Root of 497?

The square root of 497 is 22.2934968096. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√497 = 22.2934968096
CalculatedNon-perfect squareIrrational
Exact form√497
Perfect squareNo
Number typeIrrational
Verification22.29349680962 ≈ 497

On this page

How the answer is calculated

We solve x2 = 497. The resulting value is x = 22.2934968096.

Verification: 22.29349680962 ≈ 497.

Simplified radical form

The square root of 497 in simplified radical form is √497.

There are no square factors that can be taken outside the radical, so √497 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal22484
Upper or equal23529

Nearby square roots

NumberSquare root
√49422.2261107709
√49522.2485954613
√49622.2710574513
√49722.2934968096
√49822.3159136044
√49922.3383079037
√50022.360679775

Number properties

Is 497 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√497 is irrational because 497 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 497.