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What is the Square Root of 782?

The square root of 782 is 27.9642629082. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√782 = 27.9642629082
CalculatedNon-perfect squareIrrational
Exact form√782
Perfect squareNo
Number typeIrrational
Verification27.96426290822 ≈ 782

On this page

How the answer is calculated

We solve x2 = 782. The resulting value is x = 27.9642629082.

Verification: 27.96426290822 ≈ 782.

Simplified radical form

The square root of 782 in simplified radical form is √782.

There are no square factors that can be taken outside the radical, so √782 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal27729
Upper or equal28784

Nearby square roots

NumberSquare root
√77927.9105714739
√78027.9284800875
√78127.946377225
√78227.9642629082
√78327.9821371593
√78428
√78528.0178514522

Number properties

Is 782 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√782 is irrational because 782 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 782.