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What is the Square Root of 180?

The square root of 180 is 13.416407865. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√180 = 13.416407865
CalculatedNon-perfect squareIrrational
Exact form√180
Perfect squareNo
Number typeIrrational
Verification13.4164078652 ≈ 180

On this page

How the answer is calculated

We solve x2 = 180. The resulting value is x = 13.416407865.

Verification: 13.4164078652 ≈ 180.

Simplified radical form

The square root of 180 in simplified radical form is 6√5.

This is equivalent to √180, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal13169
Upper or equal14196

Nearby square roots

NumberSquare root
√17713.3041346957
√17813.3416640641
√17913.3790881603
√18013.416407865
√18113.4536240471
√18213.4907375632
√18313.5277492585

Number properties

Is 180 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√180 is irrational because 180 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 180.