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What is the Square Root of 1309?

The square root of 1309 is 36.1801050303. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√1309 = 36.1801050303
CalculatedNon-perfect squareIrrational
Exact form√1309
Perfect squareNo
Number typeIrrational
Verification36.18010503032 ≈ 1309

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How the answer is calculated

We solve x2 = 1309. The resulting value is x = 36.1801050303.

Verification: 36.18010503032 ≈ 1309.

Simplified radical form

The square root of 1309 in simplified radical form is √1309.

There are no square factors that can be taken outside the radical, so √1309 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal361296
Upper or equal371369

Nearby square roots

NumberSquare root
√130636.1386219992
√130736.1524549651
√130836.1662826401
√130936.1801050303
√131036.1939221417
√131136.2077339805
√131236.2215405525

Number properties

Is 1309 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√1309 is irrational because 1309 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 1309.