6.5-6.7 Radical Expressions/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+2).

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs (for square roots) or groups (for cube roots) to simplify.

Front

What is the square root of a number?

Back

The square root of a number 'x' is a value 'y' such that y² = x. For example, √9 = 3 because 3² = 9.

Front

What does it mean to solve a radical equation?

Back

Solving a radical equation involves isolating the radical on one side and then squaring both sides to eliminate the radical, followed by solving the resulting equation.

Front

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

Back

The principle states that if two expressions are equal, 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 your solution for a radical equation?

Back

To check your solution, substitute the solution back into the original equation to verify if both sides are equal.

Front

What is the difference between a radical and an exponent?

Back

A radical represents the root of a number, while an exponent indicates how many times a number is multiplied by itself. For example, √x is a radical, and x² is an exponent.

Front

How do you rewrite a radical expression in exponential form?

Back

To rewrite a radical expression in exponential form, use the property that √x = x^(1/2) and ∛x = x^(1/3).

Front

What is the product property of radicals?

Back

The product property states that √(a*b) = √a * √b, allowing the simplification of the product of two radicals.