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What is the Square Root of 13757?

The square root of 13757 is 117.290238298. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√13757 = 117.290238298
CalculatedNon-perfect squareIrrational
Exact form√13757
Perfect squareNo
Number typeIrrational
Verification117.2902382982 ≈ 13757

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How the answer is calculated

We solve x2 = 13757. The resulting value is x = 117.290238298.

Verification: 117.2902382982 ≈ 13757.

Simplified radical form

The square root of 13757 in simplified radical form is √13757.

There are no square factors that can be taken outside the radical, so √13757 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal11713689
Upper or equal11813924

Nearby square roots

NumberSquare root
√13754117.2774488126
√13755117.2817121294
√13756117.2859752912
√13757117.290238298
√13758117.2945011499
√13759117.2987638469
√13760117.3030263889

Number properties

Is 13757 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√13757 is irrational because 13757 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 13757.