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What is the Square Root of 463?

The square root of 463 is 21.5174347914. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√463 = 21.5174347914
CalculatedNon-perfect squareIrrational
Exact form√463
Perfect squareNo
Number typeIrrational
Verification21.51743479142 ≈ 463

On this page

How the answer is calculated

We solve x2 = 463. The resulting value is x = 21.5174347914.

Verification: 21.51743479142 ≈ 463.

Simplified radical form

The square root of 463 in simplified radical form is √463.

There are no square factors that can be taken outside the radical, so √463 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal21441
Upper or equal22484

Nearby square roots

NumberSquare root
√46021.4476105895
√46121.4709105536
√46221.4941852602
√46321.5174347914
√46421.5406592285
√46521.5638586528
√46621.5870331449

Number properties

Is 463 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√463 is irrational because 463 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 463.