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What is the Square Root of 1680?

The square root of 1680 is 40.9878030638. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√1680 = 40.9878030638
CalculatedNon-perfect squareIrrational
Exact form√1680
Perfect squareNo
Number typeIrrational
Verification40.98780306382 ≈ 1680

On this page

How the answer is calculated

We solve x2 = 1680. The resulting value is x = 40.9878030638.

Verification: 40.98780306382 ≈ 1680.

Simplified radical form

The square root of 1680 in simplified radical form is 4√105.

This is equivalent to √1680, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal401600
Upper or equal411681

Nearby square roots

NumberSquare root
√167740.9511904589
√167840.9633982965
√167940.9756024971
√168040.9878030638
√168141
√168241.0121933088
√168341.0243829935

Number properties

Is 1680 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√1680 is irrational because 1680 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 1680.