Solving Square Root Equations

A square root equation is an equation that contains a variable within a square root. It can often be solved by isolating the square root and then squaring both sides of the equation.

To isolate a square root, you need to move all other terms to the opposite side of the equation. For example, in $$\text{if } \sqrt{x} = 3, \text{ then } x = 3^2 = 9$$ .

The first step is to add 8 to both sides of the equation to isolate the square root: $$\text{if } \sqrt{x+13} = 6$$ .

The solution is $$x = 23$$ .

An equation has 'no solution' if there are no values for the variable that satisfy the equation. For example, $$\text{if } \sqrt{x} = -1$$ has no solution since the square root cannot be negative.

To check if a solution is valid, substitute the solution back into the original equation to see if both sides are equal.

The solution is $$x = 3$$ .

First, divide both sides by 2 to isolate the square root: $$\text{ }\sqrt{x+1} = 2$$ , then square both sides to solve for x.

The solution is $$x = 3$$ .

Squaring both sides of an equation helps eliminate the square root, allowing you to solve for the variable more easily.