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What is the Square Root of 521?

The square root of 521 is 22.825424421. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√521 = 22.825424421
CalculatedNon-perfect squareIrrational
Exact form√521
Perfect squareNo
Number typeIrrational
Verification22.8254244212 ≈ 521

On this page

How the answer is calculated

We solve x2 = 521. The resulting value is x = 22.825424421.

Verification: 22.8254244212 ≈ 521.

Simplified radical form

The square root of 521 in simplified radical form is √521.

There are no square factors that can be taken outside the radical, so √521 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal22484
Upper or equal23529

Nearby square roots

NumberSquare root
√51822.7596133535
√51922.7815714998
√52022.803508502
√52122.825424421
√52222.8473193176
√52322.8691932521
√52422.8910462845

Number properties

Is 521 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√521 is irrational because 521 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 521.