Solving Square Root Equations

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

To isolate the square root, you can move all other terms to the opposite side of the equation. For example, in the equation √x = 5, you would square both sides to eliminate the square root.

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

To check if a solution is extraneous, substitute it back into the original equation. If it does not satisfy the equation, it is considered extraneous.

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

When you square both sides of an equation, you eliminate the square root, but you may introduce extraneous solutions.

The solution is x = 32, found by squaring both sides: x + 4 = 36, then x = 36 - 4.

There is no solution, as the square root cannot equal a negative number.

A square root equation can have zero, one, or two solutions, depending on the equation.

The solution is x = 0, as the square root of zero is zero.