Rationalizing Denominators and Roots

The video tutorial explains how to rationalize a denominator containing a radical with a fifth root. It introduces the property of nth roots and powers, showing how they can be used to rewrite expressions without radicals in the denominator. The tutorial demonstrates factoring and multiplying to achieve the desired form, ultimately simplifying the expression and rationalizing the denominator.

What is the main goal when rationalizing the denominator?

• To add more radicals to the expression

• To factor the numerator

• To rewrite the expression without a radical in the denominator

• To eliminate the numerator

What is the first step in rationalizing the denominator?

• Factor the denominator

• Multiply the numerator by zero

• Add more radicals

• Divide the numerator by the denominator

What is the main goal when rationalizing the denominator?

• To factor the numerator

• To rewrite the expression without a radical in the denominator

• To eliminate the numerator

• To add more radicals to the expression

What does the property of nth roots state?

• The nth root of a number is always negative

• The nth root of a base to the nth power is the base itself

• The nth root of a base to the nth power is undefined

• The nth root of a base to the nth power is zero

What happens when the index and power in a radical match?

• They cancel each other out

• They double the value

• They become zero

• They become negative

What does the property of nth roots state?

• The nth root of a number is always negative

• The nth root of a base to the nth power is the base itself

• The nth root of a base to the nth power is zero

• The nth root of a base to the nth power is undefined

What are the prime factors of 9?

• 7 * 7

• 3 * 3

• 2 * 2

• 5 * 5

What is the purpose of factoring the denominator?

• To make the expression more complex

• To add more radicals

• To identify the prime factors

• To eliminate the numerator

Why do we multiply the numerator and denominator by another fifth root?

• To eliminate the numerator

• To change the value of the expression

• To make the expression more complex

• To ensure the exponents in the denominator match the index

What is the purpose of multiplying the numerator and denominator by another fifth root?

• To ensure the exponents in the denominator match the index

• To change the value of the expression

• To make the expression more complex

• To eliminate the numerator