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What is the Square Root of 506?

The square root of 506 is 22.4944437584. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√506 = 22.4944437584
CalculatedNon-perfect squareIrrational
Exact form√506
Perfect squareNo
Number typeIrrational
Verification22.49444375842 ≈ 506

On this page

How the answer is calculated

We solve x2 = 506. The resulting value is x = 22.4944437584.

Verification: 22.49444375842 ≈ 506.

Simplified radical form

The square root of 506 in simplified radical form is √506.

There are no square factors that can be taken outside the radical, so √506 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal22484
Upper or equal23529

Nearby square roots

NumberSquare root
√50322.427661492
√50422.4499443206
√50522.4722050542
√50622.4944437584
√50722.5166604984
√50822.5388553392
√50922.5610283454

Number properties

Is 506 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√506 is irrational because 506 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 506.