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What is the Square Root of 13509?

The square root of 13509 is 116.2282237669. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√13509 = 116.2282237669
CalculatedNon-perfect squareIrrational
Exact form√13509
Perfect squareNo
Number typeIrrational
Verification116.22822376692 ≈ 13509

On this page

How the answer is calculated

We solve x2 = 13509. The resulting value is x = 116.2282237669.

Verification: 116.22822376692 ≈ 13509.

Simplified radical form

The square root of 13509 in simplified radical form is 3√1501.

This is equivalent to √13509, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal11613456
Upper or equal11713689

Nearby square roots

NumberSquare root
√13506116.215317407
√13507116.2196196862
√13508116.2239218061
√13509116.2282237669
√13510116.2325255684
√13511116.2368272107
√13512116.2411286938

Number properties

Is 13509 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√13509 is irrational because 13509 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 13509.