Solving Square Root Equations

Front

What is a square root equation?

Back

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.

Front

How do you isolate the square root in an equation?

Back

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.

Front

What is an extraneous solution?

Back

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

Front

How do you check if a solution is extraneous?

Back

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.

Front

What is the first step in solving a square root equation?

Back

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

Front

What happens when you square both sides of an equation?

Back

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

Front

What is the solution to the equation √(x + 4) = 6?

Back

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

Front

What is the solution to the equation √(x - 1) = -3?

Back

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

Front

How many solutions can a square root equation have?

Back

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

Front

What is the solution to the equation √(x) = 0?

Back

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