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What is the Square Root of 1564?

The square root of 1564 is 39.5474398666. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√1564 = 39.5474398666
CalculatedNon-perfect squareIrrational
Exact form√1564
Perfect squareNo
Number typeIrrational
Verification39.54743986662 ≈ 1564

On this page

How the answer is calculated

We solve x2 = 1564. The resulting value is x = 39.5474398666.

Verification: 39.54743986662 ≈ 1564.

Simplified radical form

The square root of 1564 in simplified radical form is 2√391.

This is equivalent to √1564, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal391521
Upper or equal401600

Nearby square roots

NumberSquare root
√156139.5094925303
√156239.5221456907
√156339.5347948015
√156439.5474398666
√156539.5600808897
√156639.5727178748
√156739.5853508258

Number properties

Is 1564 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√1564 is irrational because 1564 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 1564.