How to rationalize the radical to evaluate a limit

The video tutorial explains how to handle radicals in fractions by using conjugates. It highlights the importance of multiplying by the conjugate to eliminate radicals and discusses why direct substitution may not work in certain cases. The tutorial walks through the multiplication and simplification process, emphasizing the cancellation of middle terms. Finally, it demonstrates the evaluation of the expression as the variable approaches a specific value, ensuring a clear understanding of the mathematical concepts involved.

Why is it important to multiply by the conjugate when dealing with radicals in fractions?

• To make the fraction more complex

• To change the sign of the expression

• To increase the value of the fraction

• To eliminate radicals and simplify the expression

What happens to the middle terms when multiplying conjugates?

• They cancel out

• They double in value

• They become negative

• They remain unchanged

Why is it unnecessary to focus on the middle terms during multiplication of conjugates?

• They are irrelevant to the final result

• They cancel out, simplifying the expression

• They are already simplified

• They are always zero

What is the result of directly substituting as X approaches 3 in the given expression?

• 1/2

• 1/4

• 1/3

• 1

What is the final value obtained after evaluating the expression as X approaches 3?

• 1/2

• 1/4

• 1/3

• 1