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What is the Square Root of 21764?

The square root of 21764 is 147.5262688473. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√21764 = 147.5262688473
CalculatedNon-perfect squareIrrational
Exact form√21764
Perfect squareNo
Number typeIrrational
Verification147.52626884732 ≈ 21764

On this page

How the answer is calculated

We solve x2 = 21764. The resulting value is x = 147.5262688473.

Verification: 147.52626884732 ≈ 21764.

Simplified radical form

The square root of 21764 in simplified radical form is 2√5441.

This is equivalent to √21764, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal14721609
Upper or equal14821904

Nearby square roots

NumberSquare root
√21761147.5161008161
√21762147.5194902377
√21763147.5228795814
√21764147.5262688473
√21765147.5296580353
√21766147.5330471454
√21767147.5364361776

Number properties

Is 21764 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√21764 is irrational because 21764 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 21764.