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What is the Square Root of 637?

The square root of 637 is 25.2388589282. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√637 = 25.2388589282
CalculatedNon-perfect squareIrrational
Exact form√637
Perfect squareNo
Number typeIrrational
Verification25.23885892822 ≈ 637

On this page

How the answer is calculated

We solve x2 = 637. The resulting value is x = 25.2388589282.

Verification: 25.23885892822 ≈ 637.

Simplified radical form

The square root of 637 in simplified radical form is 7√13.

This is equivalent to √637, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal25625
Upper or equal26676

Nearby square roots

NumberSquare root
√63425.179356624
√63525.1992063367
√63625.2190404258
√63725.2388589282
√63825.2586618806
√63925.2784493195
√64025.2982212813

Number properties

Is 637 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√637 is irrational because 637 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 637.