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What is the Square Root of 312?

The square root of 312 is 17.6635217327. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√312 = 17.6635217327
CalculatedNon-perfect squareIrrational
Exact form√312
Perfect squareNo
Number typeIrrational
Verification17.66352173272 ≈ 312

On this page

How the answer is calculated

We solve x2 = 312. The resulting value is x = 17.6635217327.

Verification: 17.66352173272 ≈ 312.

Simplified radical form

The square root of 312 in simplified radical form is 2√78.

This is equivalent to √312, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal17289
Upper or equal18324

Nearby square roots

NumberSquare root
√30917.5783958312
√31017.6068168617
√31117.6351920885
√31217.6635217327
√31317.691806013
√31417.7200451467
√31517.7482393493

Number properties

Is 312 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√312 is irrational because 312 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 312.