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 often 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 = a + b, you would rearrange it to √x = a + b.

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 do you do after isolating the square root in an equation?

Back

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

Front

What is the importance of checking your solutions in square root equations?

Back

It is important to check your solutions because squaring both sides of an equation can introduce extraneous solutions that do not satisfy the original equation.

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 can you solve the equation √(x + 3) = 7?

Back

To solve √(x + 3) = 7, square both sides to get x + 3 = 49, then isolate x to find x = 46.

Front

What is the solution to the equation √(x) = 5?

Back

The solution is x = 25, since squaring both sides gives x = 5^2.

Front

What is the domain of a square root function?

Back

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

Front

How do you solve the equation √(x - 1) = 6?

Back

Square both sides to get x - 1 = 36, then isolate x to find x = 37.