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What is the Square Root of 3006?

The square root of 3006 is 54.8270006475. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√3006 = 54.8270006475
CalculatedNon-perfect squareIrrational
Exact form√3006
Perfect squareNo
Number typeIrrational
Verification54.82700064752 ≈ 3006

On this page

How the answer is calculated

We solve x2 = 3006. The resulting value is x = 54.8270006475.

Verification: 54.82700064752 ≈ 3006.

Simplified radical form

The square root of 3006 in simplified radical form is 3√334.

This is equivalent to √3006, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal542916
Upper or equal553025

Nearby square roots

NumberSquare root
√300354.7996350353
√300454.8087584242
√300554.8178802947
√300654.8270006475
√300754.8361194834
√300854.8452368032
√300954.8543526076

Number properties

Is 3006 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√3006 is irrational because 3006 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 3006.