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What is the Square Root of 157?

The square root of 157 is 12.5299640861. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√157 = 12.5299640861
CalculatedNon-perfect squareIrrational
Exact form√157
Perfect squareNo
Number typeIrrational
Verification12.52996408612 ≈ 157

On this page

How the answer is calculated

We solve x2 = 157. The resulting value is x = 12.5299640861.

Verification: 12.52996408612 ≈ 157.

Simplified radical form

The square root of 157 in simplified radical form is √157.

There are no square factors that can be taken outside the radical, so √157 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal12144
Upper or equal13169

Nearby square roots

NumberSquare root
√15412.409673646
√15512.449899598
√15612.4899959968
√15712.5299640861
√15812.56980509
√15912.6095202129
√16012.6491106407

Number properties

Is 157 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√157 is irrational because 157 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 157.