Infolity
  1. Home
  2. Calculators
  3. Square Root

What is the Square Root of 12000?

The square root of 12000 is 109.544511501. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√12000 = 109.544511501
CalculatedNon-perfect squareIrrational
Exact form√12000
Perfect squareNo
Number typeIrrational
Verification109.5445115012 ≈ 12000

On this page

How the answer is calculated

We solve x2 = 12000. The resulting value is x = 109.544511501.

Verification: 109.5445115012 ≈ 12000.

Simplified radical form

The square root of 12000 in simplified radical form is 20√30.

This is equivalent to √12000, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal10911881
Upper or equal11012100

Nearby square roots

NumberSquare root
√11997109.5308175812
√11998109.5353824113
√11999109.5399470513
√12000109.544511501
√12001109.5490757606
√12002109.55363983
√12003109.5582037093

Number properties

Is 12000 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√12000 is irrational because 12000 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 12000.