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What is the Square Root of 824?

The square root of 824 is 28.7054001888. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√824 = 28.7054001888
CalculatedNon-perfect squareIrrational
Exact form√824
Perfect squareNo
Number typeIrrational
Verification28.70540018882 ≈ 824

On this page

How the answer is calculated

We solve x2 = 824. The resulting value is x = 28.7054001888.

Verification: 28.70540018882 ≈ 824.

Simplified radical form

The square root of 824 in simplified radical form is 2√206.

This is equivalent to √824, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal28784
Upper or equal29841

Nearby square roots

NumberSquare root
√82128.6530975638
√82228.6705423737
√82328.6879765756
√82428.7054001888
√82528.7228132327
√82628.7402157264
√82728.7576076891

Number properties

Is 824 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√824 is irrational because 824 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 824.