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What is the Square Root of 306?

The square root of 306 is 17.4928556845. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√306 = 17.4928556845
CalculatedNon-perfect squareIrrational
Exact form√306
Perfect squareNo
Number typeIrrational
Verification17.49285568452 ≈ 306

On this page

How the answer is calculated

We solve x2 = 306. The resulting value is x = 17.4928556845.

Verification: 17.49285568452 ≈ 306.

Simplified radical form

The square root of 306 in simplified radical form is 3√34.

This is equivalent to √306, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal17289
Upper or equal18324

Nearby square roots

NumberSquare root
√30317.4068951855
√30417.4355957742
√30517.4642491966
√30617.4928556845
√30717.5214154679
√30817.5499287748
√30917.5783958312

Number properties

Is 306 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√306 is irrational because 306 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 306.