Mastering Rationalizing Denominators with Conjugates

This video tutorial explains how to use conjugates to rationalize denominators in fractions. It begins with an introduction to conjugates, which are expressions with opposite signs. The video demonstrates how to multiply both the numerator and denominator by the conjugate to eliminate radicals in the denominator. Two example problems are solved step-by-step, showing the process of simplifying expressions using conjugates. The tutorial concludes with tips on writing down steps to simplify complex calculations.

Why is it important to rationalize the denominator of a fraction?

• To make the fraction easier to read

• To make the numerator a whole number

• To eliminate the radical from the denominator

• To change the value of the fraction

What is a conjugate in the context of rationalizing denominators?

• Two expressions with the same signs

• Two expressions with opposite signs

• Two identical expressions

• Two expressions with different variables

If the denominator is 5 + √2, what is its conjugate?

• √2 + 5

• √2 - 5

• 5 - √2

• 5 + √2

When multiplying by the conjugate, what must you remember to do?

• Add the conjugate to the fraction

• Multiply both the numerator and the denominator

• Only multiply the numerator

• Only multiply the denominator

What happens to the middle terms when you multiply conjugates?

• They add up

• They cancel out

• They double

• They remain unchanged

In the first example, what is the simplified form of the denominator after rationalizing 5 + √2?

• 2

• 23

• 25

• 10

In the second example, what is the conjugate of √2 + √5?

• √2 + √5

• √2 - √5

• √5 + √2

• √5 - √2

What is the simplified form of √50?

• 2√5

• 5√2

• √25

• 10

What is the final simplified form of the fraction in the second example?

• √5

• 2√5

• √2

• 3√2

What is a key tip for solving problems involving rationalizing denominators?

• Skip the simplification step

• Do everything in your head

• Use a calculator for every step

• Write everything down