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What is the Square Root of 314?

The square root of 314 is 17.7200451467. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√314 = 17.7200451467
CalculatedNon-perfect squareIrrational
Exact form√314
Perfect squareNo
Number typeIrrational
Verification17.72004514672 ≈ 314

On this page

How the answer is calculated

We solve x2 = 314. The resulting value is x = 17.7200451467.

Verification: 17.72004514672 ≈ 314.

Simplified radical form

The square root of 314 in simplified radical form is √314.

There are no square factors that can be taken outside the radical, so √314 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal17289
Upper or equal18324

Nearby square roots

NumberSquare root
√31117.6351920885
√31217.6635217327
√31317.691806013
√31417.7200451467
√31517.7482393493
√31617.7763888346
√31717.8044938148

Number properties

Is 314 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√314 is irrational because 314 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 314.