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What is the Square Root of 75?

The square root of 75 is 8.6602540378. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√75 = 8.6602540378
CalculatedNon-perfect squareIrrational
Exact form√75
Perfect squareNo
Number typeIrrational
Verification8.66025403782 ≈ 75

On this page

How the answer is calculated

We solve x2 = 75. The resulting value is x = 8.6602540378.

Verification: 8.66025403782 ≈ 75.

Simplified radical form

The square root of 75 in simplified radical form is 5√3.

This is equivalent to √75, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal864
Upper or equal981

Nearby square roots

NumberSquare root
√728.4852813742
√738.5440037453
√748.602325267
√758.6602540378
√768.7177978871
√778.7749643874
√788.8317608663

Number properties

Is 75 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√75 is irrational because 75 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 75.