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What is the Square Root of 461?

The square root of 461 is 21.4709105536. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√461 = 21.4709105536
CalculatedNon-perfect squareIrrational
Exact form√461
Perfect squareNo
Number typeIrrational
Verification21.47091055362 ≈ 461

On this page

How the answer is calculated

We solve x2 = 461. The resulting value is x = 21.4709105536.

Verification: 21.47091055362 ≈ 461.

Simplified radical form

The square root of 461 in simplified radical form is √461.

There are no square factors that can be taken outside the radical, so √461 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal21441
Upper or equal22484

Nearby square roots

NumberSquare root
√45821.400934559
√45921.4242852856
√46021.4476105895
√46121.4709105536
√46221.4941852602
√46321.5174347914
√46421.5406592285

Number properties

Is 461 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√461 is irrational because 461 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 461.