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What is the Square Root of 13824?

The square root of 13824 is 117.5755076536. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√13824 = 117.5755076536
CalculatedNon-perfect squareIrrational
Exact form√13824
Perfect squareNo
Number typeIrrational
Verification117.57550765362 ≈ 13824

On this page

How the answer is calculated

We solve x2 = 13824. The resulting value is x = 117.5755076536.

Verification: 117.57550765362 ≈ 13824.

Simplified radical form

The square root of 13824 in simplified radical form is 48√6.

This is equivalent to √13824, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal11713689
Upper or equal11813924

Nearby square roots

NumberSquare root
√13821117.5627492023
√13822117.5670021732
√13823117.5712549903
√13824117.5755076536
√13825117.579760163
√13826117.5840125187
√13827117.5882647206

Number properties

Is 13824 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√13824 is irrational because 13824 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 13824.