Infolity
  1. Home
  2. Calculators
  3. Square Root

What is the Square Root of 420?

The square root of 420 is 20.4939015319. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√420 = 20.4939015319
CalculatedNon-perfect squareIrrational
Exact form√420
Perfect squareNo
Number typeIrrational
Verification20.49390153192 ≈ 420

On this page

How the answer is calculated

We solve x2 = 420. The resulting value is x = 20.4939015319.

Verification: 20.49390153192 ≈ 420.

Simplified radical form

The square root of 420 in simplified radical form is 2√105.

This is equivalent to √420, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal20400
Upper or equal21441

Nearby square roots

NumberSquare root
√41720.4205778567
√41820.4450483003
√41920.4694894905
√42020.4939015319
√42120.5182845287
√42220.5426385842
√42320.5669638012

Number properties

Is 420 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√420 is irrational because 420 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 420.