Q:

# How do you extract square roots?

A:

A method of solving quadratic equations is to extract the roots. This means that the possible values of x are determined by finding the square root of both sides of the equation.

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1. Rearrange the given equation

Determine if the equation is in the form that allows for both sides of it to be manipulated. If the given equation is (x - 2)^2 - 8 = 0, rearrange it so that the 8 is on the right hand side: (x-2)^2 = 8.

2. Find the square root of both sides

Take the square root of both sides and rewrite the equation: (x - 2) = (+/-)_sqrt(8). If the right-hand side of the equation is not a perfect square, reduce the radicand to a factor that is a perfect square. The factors of 8 are 2 and 4, and 4 is a perfect square. Thus, the equation ends up as (x - 2) = (+/-)_2 * sqrt(2).

3. Solve for x

Solve the equation for x. There are two answers for x because of the (+/-) and because the equation is to the power of 2. The answers are x = 2 + 2 * sqrt(2) and x = 2 - 2 * sqrt(2).

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