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What is the Square Root of 309?

The square root of 309 is 17.5783958312. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√309 = 17.5783958312
CalculatedNon-perfect squareIrrational
Exact form√309
Perfect squareNo
Number typeIrrational
Verification17.57839583122 ≈ 309

On this page

How the answer is calculated

We solve x2 = 309. The resulting value is x = 17.5783958312.

Verification: 17.57839583122 ≈ 309.

Simplified radical form

The square root of 309 in simplified radical form is √309.

There are no square factors that can be taken outside the radical, so √309 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal17289
Upper or equal18324

Nearby square roots

NumberSquare root
√30617.4928556845
√30717.5214154679
√30817.5499287748
√30917.5783958312
√31017.6068168617
√31117.6351920885
√31217.6635217327

Number properties

Is 309 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√309 is irrational because 309 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 309.