How do you extract square roots?

By Forinfos - 30/05/2025 - 0 comments

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.

  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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