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What is the Square Root of 564?

The square root of 564 is 23.7486841741. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√564 = 23.7486841741
CalculatedNon-perfect squareIrrational
Exact form√564
Perfect squareNo
Number typeIrrational
Verification23.74868417412 ≈ 564

On this page

How the answer is calculated

We solve x2 = 564. The resulting value is x = 23.7486841741.

Verification: 23.74868417412 ≈ 564.

Simplified radical form

The square root of 564 in simplified radical form is 2√141.

This is equivalent to √564, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal23529
Upper or equal24576

Nearby square roots

NumberSquare root
√56123.6854385647
√56223.7065391823
√56323.7276210354
√56423.7486841741
√56523.769728648
√56623.7907545067
√56723.8117617996

Number properties

Is 564 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√564 is irrational because 564 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 564.