A2 Solving Square Root Equations

A square root equation is an equation that involves a variable under a square root, typically in the form √x = a.

To isolate the square root, you can move all other terms to the opposite side of the equation.

Square both sides of the equation to eliminate the square root: x = 5².

x = 25.

It means that there are no real numbers that satisfy the equation, often occurring when a negative number is under the square root.

Substitute the solution back into the original equation to see if both sides are equal.

x = 0.

Squaring both sides can introduce extraneous solutions, so it's important to check all potential solutions.

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

x = 10.