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What is the Square Root of 1509?

The square root of 1509 is 38.8458491991. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√1509 = 38.8458491991
CalculatedNon-perfect squareIrrational
Exact form√1509
Perfect squareNo
Number typeIrrational
Verification38.84584919912 ≈ 1509

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How the answer is calculated

We solve x2 = 1509. The resulting value is x = 38.8458491991.

Verification: 38.84584919912 ≈ 1509.

Simplified radical form

The square root of 1509 in simplified radical form is √1509.

There are no square factors that can be taken outside the radical, so √1509 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal381444
Upper or equal391521

Nearby square roots

NumberSquare root
√150638.8072158239
√150738.8200978876
√150838.8329756779
√150938.8458491991
√151038.8587184555
√151138.8715834512
√151238.8844441904

Number properties

Is 1509 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√1509 is irrational because 1509 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 1509.