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What is the Square Root of 205?

The square root of 205 is 14.3178210633. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√205 = 14.3178210633
CalculatedNon-perfect squareIrrational
Exact form√205
Perfect squareNo
Number typeIrrational
Verification14.31782106332 ≈ 205

On this page

How the answer is calculated

We solve x2 = 205. The resulting value is x = 14.3178210633.

Verification: 14.31782106332 ≈ 205.

Simplified radical form

The square root of 205 in simplified radical form is √205.

There are no square factors that can be taken outside the radical, so √205 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal14196
Upper or equal15225

Nearby square roots

NumberSquare root
√20214.2126704036
√20314.2478068488
√20414.2828568571
√20514.3178210633
√20614.3527000944
√20714.3874945699
√20814.4222051019

Number properties

Is 205 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√205 is irrational because 205 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 205.