Solving Square Root Equations

A square root equation is an equation that involves a variable within a square root. It can typically be expressed in the form √x = a, where x is the variable and a is a constant.

To isolate the square root in an equation, you can move all other terms to the opposite side of the equation. For example, if you have √x = b + c, you would rearrange it to √x = b + c.

The first step in solving a square root equation is to isolate the square root on one side of the equation.

After isolating the square root, you square both sides of the equation to eliminate the square root.

It is important to check your solutions in square root equations because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

To solve √(x + 5) = 7, first square both sides to get x + 5 = 49. Then, subtract 5 from both sides to find x = 44.

To solve √(x) = 6, square both sides to get x = 36.

To solve x^2 = 25, take the square root of both sides, giving x = 5 or x = -5.

The domain of a square root function is the set of all real numbers x such that the expression under the square root is non-negative (x ≥ 0).