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What is the Square Root of 2564?

The square root of 2564 is 50.6359556047. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√2564 = 50.6359556047
CalculatedNon-perfect squareIrrational
Exact form√2564
Perfect squareNo
Number typeIrrational
Verification50.63595560472 ≈ 2564

On this page

How the answer is calculated

We solve x2 = 2564. The resulting value is x = 50.6359556047.

Verification: 50.63595560472 ≈ 2564.

Simplified radical form

The square root of 2564 in simplified radical form is 2√641.

This is equivalent to √2564, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal502500
Upper or equal512601

Nearby square roots

NumberSquare root
√256150.6063237155
√256250.6162029394
√256350.6260802354
√256450.6359556047
√256550.6458290484
√256650.6557005677
√256750.6655701636

Number properties

Is 2564 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√2564 is irrational because 2564 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 2564.