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What is the Square Root of 2164?

The square root of 2164 is 46.5188133985. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√2164 = 46.5188133985
CalculatedNon-perfect squareIrrational
Exact form√2164
Perfect squareNo
Number typeIrrational
Verification46.51881339852 ≈ 2164

On this page

How the answer is calculated

We solve x2 = 2164. The resulting value is x = 46.5188133985.

Verification: 46.51881339852 ≈ 2164.

Simplified radical form

The square root of 2164 in simplified radical form is 2√541.

This is equivalent to √2164, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal462116
Upper or equal472209

Nearby square roots

NumberSquare root
√216146.4865571967
√216246.4973117503
√216346.5080638169
√216446.5188133985
√216546.5295604965
√216646.5403051129
√216746.5510472492

Number properties

Is 2164 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√2164 is irrational because 2164 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 2164.