# Distinguish between square roots and factoring.

A) What is the square root property and what is it used for? In what form should an equation be in order to use the square root property? When should the square root property be used instead of factoring? Use the following to explain.

9x^2-12x+4=27

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

The square root property is one method that is used to find the solutions to a quadratic (second degree) equation. This method involves taking the square roots of both sides of the equation.

Before taking the square root of each side, you must isolate the term that contains the squared variable. Once this squared-variable term is fully isolated, you will take the square root of both sides and solve for the variable.

We should use the square root property instead of using factoring when we want to determine what single number is a component of the result.

For example, 9x^2-12x+4=27 -> (3x-2)^2=27, so 3x-2=3sqrt(3) or 3x-2=-3sqrt(3). Hence, the root is x=[3sqrt(3)+2]/3 or x=[-3sqrt(3)+2]/3

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