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What is the Square Root of 414?

The square root of 414 is 20.3469899494. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√414 = 20.3469899494
CalculatedNon-perfect squareIrrational
Exact form√414
Perfect squareNo
Number typeIrrational
Verification20.34698994942 ≈ 414

On this page

How the answer is calculated

We solve x2 = 414. The resulting value is x = 20.3469899494.

Verification: 20.34698994942 ≈ 414.

Simplified radical form

The square root of 414 in simplified radical form is 3√46.

This is equivalent to √414, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal20400
Upper or equal21441

Nearby square roots

NumberSquare root
√41120.2731349327
√41220.2977831302
√41320.3224014329
√41420.3469899494
√41520.3715487875
√41620.3960780544
√41720.4205778567

Number properties

Is 414 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√414 is irrational because 414 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 414.