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What is the Square Root of 458?

The square root of 458 is 21.400934559. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√458 = 21.400934559
CalculatedNon-perfect squareIrrational
Exact form√458
Perfect squareNo
Number typeIrrational
Verification21.4009345592 ≈ 458

On this page

How the answer is calculated

We solve x2 = 458. The resulting value is x = 21.400934559.

Verification: 21.4009345592 ≈ 458.

Simplified radical form

The square root of 458 in simplified radical form is √458.

There are no square factors that can be taken outside the radical, so √458 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal21441
Upper or equal22484

Nearby square roots

NumberSquare root
√45521.3307290077
√45621.3541565041
√45721.3775583264
√45821.400934559
√45921.4242852856
√46021.4476105895
√46121.4709105536

Number properties

Is 458 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√458 is irrational because 458 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 458.