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What is the Square Root of 512?

The square root of 512 is 22.627416998. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√512 = 22.627416998
CalculatedNon-perfect squareIrrational
Exact form√512
Perfect squareNo
Number typeIrrational
Verification22.6274169982 ≈ 512

On this page

How the answer is calculated

We solve x2 = 512. The resulting value is x = 22.627416998.

Verification: 22.6274169982 ≈ 512.

Simplified radical form

The square root of 512 in simplified radical form is 16√2.

This is equivalent to √512, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal22484
Upper or equal23529

Nearby square roots

NumberSquare root
√50922.5610283454
√51022.5831795813
√51122.6053091109
√51222.627416998
√51322.6495033058
√51422.6715680975
√51522.6936114358

Number properties

Is 512 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√512 is irrational because 512 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 512.