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What is the Square Root of 3213?

The square root of 3213 is 56.6833308831. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√3213 = 56.6833308831
CalculatedNon-perfect squareIrrational
Exact form√3213
Perfect squareNo
Number typeIrrational
Verification56.68333088312 ≈ 3213

On this page

How the answer is calculated

We solve x2 = 3213. The resulting value is x = 56.6833308831.

Verification: 56.68333088312 ≈ 3213.

Simplified radical form

The square root of 3213 in simplified radical form is 3√357.

This is equivalent to √3213, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal563136
Upper or equal573249

Nearby square roots

NumberSquare root
√321056.6568618969
√321156.665686266
√321256.6745092612
√321356.6833308831
√321456.6921511322
√321556.7009700093
√321656.709787515

Number properties

Is 3213 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√3213 is irrational because 3213 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 3213.