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What is the Square Root of 397?

The square root of 397 is 19.9248588452. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√397 = 19.9248588452
CalculatedNon-perfect squareIrrational
Exact form√397
Perfect squareNo
Number typeIrrational
Verification19.92485884522 ≈ 397

On this page

How the answer is calculated

We solve x2 = 397. The resulting value is x = 19.9248588452.

Verification: 19.92485884522 ≈ 397.

Simplified radical form

The square root of 397 in simplified radical form is √397.

There are no square factors that can be taken outside the radical, so √397 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal19361
Upper or equal20400

Nearby square roots

NumberSquare root
√39419.8494332413
√39519.8746069144
√39619.8997487421
√39719.9248588452
√39819.9499373433
√39919.9749843554
√40020

Number properties

Is 397 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√397 is irrational because 397 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 397.