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What is the Square Root of 421?

The square root of 421 is 20.5182845287. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√421 = 20.5182845287
CalculatedNon-perfect squareIrrational
Exact form√421
Perfect squareNo
Number typeIrrational
Verification20.51828452872 ≈ 421

On this page

How the answer is calculated

We solve x2 = 421. The resulting value is x = 20.5182845287.

Verification: 20.51828452872 ≈ 421.

Simplified radical form

The square root of 421 in simplified radical form is √421.

There are no square factors that can be taken outside the radical, so √421 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal20400
Upper or equal21441

Nearby square roots

NumberSquare root
√41820.4450483003
√41920.4694894905
√42020.4939015319
√42120.5182845287
√42220.5426385842
√42320.5669638012
√42420.591260282

Number properties

Is 421 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√421 is irrational because 421 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 421.