Solving Radical and Rational Exponent Equations

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x or ∛(x+1).

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction. For example, x^(1/2) is equivalent to √x, and x^(3/2) is equivalent to √(x^3).

Front

How do you solve an equation with a square root?

Back

To solve an equation with a square root, isolate the square root on one side and then square both sides of the equation to eliminate the square root.

Front

What is the principle of squaring both sides of an equation?

Back

The principle states that if two expressions are equal, then squaring both sides will maintain the equality, but it may introduce extraneous solutions.

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 valid?

Back

To check if a solution is valid, substitute the solution back into the original equation to see if it holds true.

Front

What is the first step in solving a rational exponent equation?

Back

The first step is to eliminate the rational exponent by raising both sides of the equation to the power of the denominator of the exponent.

Front

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means to rewrite it in its simplest form, removing any perfect squares or cubes from under the radical.

Front

How do you combine like terms in radical expressions?

Back

Like terms in radical expressions can be combined if they have the same radicand and index. For example, √2 + 2√2 = 3√2.

Front

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

Back

A radical equation contains a variable within a radical, while a rational equation involves fractions with polynomials in the numerator and denominator.