Multiply by the conjugate to simplify a radical rational expression

The video tutorial covers rationalizing denominators by multiplying by the conjugate to eliminate radicals. It explains the difference of two squares, showing how middle terms cancel out, simplifying expressions. The tutorial also applies the distributive property to multiply numerators, emphasizing the importance of these techniques in simplifying mathematical expressions.

Why is it important to rationalize the denominator when dealing with radicals?

• To make the expression more complex

• To eliminate the radical from the denominator

• To increase the value of the expression

• To simplify the numerator

What is the result of applying the difference of two squares to the expression (a + b)(a - b)?

• a^2 + b^2

• a^2 - 2ab + b^2

• a^2 - b^2

• a^2 + 2ab + b^2

When simplifying (2 + sqrt(3))(2 - sqrt(3)), what happens to the middle terms?

• They add up

• They double

• They remain unchanged

• They cancel out

What is the simplified result of multiplying sqrt(5) by 2?

• 2

• sqrt(10)

• 2 sqrt(5)

• 5

How does understanding the difference of two squares help in simplifying expressions quickly?

• It increases the complexity of the expression

• It allows for quick elimination of middle terms

• It helps in multiplying the numerator

• It makes the expression more difficult to solve