HW 4.8 and 49 Solve Radical Functions 4E1

Front

What is an extraneous solution in the context of radical equations?

Back

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

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side of the equation, square both sides to eliminate the radical, and then solve for the variable.

Front

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

Back

Squaring both sides can introduce extraneous solutions, which must be checked against the original equation.

Front

What is the nth root of a number?

Back

The nth root of a number x is a number r such that r^n = x.

Front

Solve for x: √(x + 16) = 8.

Back

x = 48.

Front

Solve for k: √(k - 90) = 0.

Back

k = 90.

Front

Simplify: √(64a^12).

Back

8a^6.

Front

Solve for n: √(n^2) = 25.

Back

n = 25 or n = -25.

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical, typically expressed as f(x) = √(g(x)).