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What is the Square Root of 208?

The square root of 208 is 14.4222051019. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√208 = 14.4222051019
CalculatedNon-perfect squareIrrational
Exact form√208
Perfect squareNo
Number typeIrrational
Verification14.42220510192 ≈ 208

On this page

How the answer is calculated

We solve x2 = 208. The resulting value is x = 14.4222051019.

Verification: 14.42220510192 ≈ 208.

Simplified radical form

The square root of 208 in simplified radical form is 4√13.

This is equivalent to √208, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal14196
Upper or equal15225

Nearby square roots

NumberSquare root
√20514.3178210633
√20614.3527000944
√20714.3874945699
√20814.4222051019
√20914.4568322948
√21014.4913767462
√21114.5258390463

Number properties

Is 208 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√208 is irrational because 208 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 208.