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What is the Square Root of 313?

The square root of 313 is 17.691806013. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√313 = 17.691806013
CalculatedNon-perfect squareIrrational
Exact form√313
Perfect squareNo
Number typeIrrational
Verification17.6918060132 ≈ 313

On this page

How the answer is calculated

We solve x2 = 313. The resulting value is x = 17.691806013.

Verification: 17.6918060132 ≈ 313.

Simplified radical form

The square root of 313 in simplified radical form is √313.

There are no square factors that can be taken outside the radical, so √313 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal17289
Upper or equal18324

Nearby square roots

NumberSquare root
√31017.6068168617
√31117.6351920885
√31217.6635217327
√31317.691806013
√31417.7200451467
√31517.7482393493
√31617.7763888346

Number properties

Is 313 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√313 is irrational because 313 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 313.