Solving Radicals Practice

Front

What is a radical equation?

Back

An equation that involves a variable within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

Isolate the radical on one side, square both sides to eliminate the radical, and solve for the variable.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving a radical equation but does not satisfy the original equation.

Front

What happens when you square both sides of a radical equation?

Back

You may introduce extraneous solutions, so always check your solutions in the original equation.

Front

What is the principal square root of a number?

Back

The non-negative root of a number; for example, the principal square root of 9 is 3.

Front

How do you check your solution in a radical equation?

Back

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

Front

What is the domain of a radical function?

Back

The set of all possible input values (x) for which the function is defined, typically where the expression under the radical is non-negative.

Front

What is the difference between a radical function and a radical equation?

Back

A radical function is a function that includes a radical expression, while a radical equation is an equation that includes a radical expression.

Front

What is the square root of a negative number?

Back

It is not a real number; it is an imaginary number, represented as 'i' times the square root of the positive value.

Front

What is the first step in solving the equation √(x + 3) = 5?

Back

Square both sides to eliminate the radical: x + 3 = 25.