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What is the Square Root of 513?

The square root of 513 is 22.6495033058. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√513 = 22.6495033058
CalculatedNon-perfect squareIrrational
Exact form√513
Perfect squareNo
Number typeIrrational
Verification22.64950330582 ≈ 513

On this page

How the answer is calculated

We solve x2 = 513. The resulting value is x = 22.6495033058.

Verification: 22.64950330582 ≈ 513.

Simplified radical form

The square root of 513 in simplified radical form is 3√57.

This is equivalent to √513, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal22484
Upper or equal23529

Nearby square roots

NumberSquare root
√51022.5831795813
√51122.6053091109
√51222.627416998
√51322.6495033058
√51422.6715680975
√51522.6936114358
√51622.7156333832

Number properties

Is 513 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√513 is irrational because 513 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 513.