 If you wanted to rationalize the denominator of the expression
√a + √b
√c − √d,
then by which factor should you multiply both the numerator and denominator?
(A) √a + √b
(B) √c + √d
(C) √c − √d
(D) √a − √b
(E) It is not possible to rationalize the denominator.

To rationalize the denominator of the expression 

\[
\frac{\sqrt{a} + \sqrt{b}}{\sqrt{c} - \sqrt{d}},
\]

you should multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of \(\sqrt{c} - \sqrt{d}\) is \(\sqrt{c} + \sqrt{d}\).

Thus, the correct factor to multiply by is:

**(B) \(\sqrt{c} + \sqrt{d}\)**.

Would you like further details or have any questions? Here are some related questions to consider:

1. What is the result of rationalizing the denominator?
2. How do you apply the conjugate in other similar expressions?
3. Can you explain why we use the conjugate to rationalize?
4. What happens if you don't rationalize the denominator?
5. Are there any cases where rationalizing is not necessary? 

**Tip:** When rationalizing, always look for the conjugate of the denominator to eliminate square roots.

If you wanted to rationalize the denominator of the expression √a + √b / √c − √d, then by which factor should you multiply both the numerator and denominator?

Learn how to rationalize the denominator of the expression √a + √b / √c − √d by multiplying by the conjugate. This guide explains the concept and provides a step-by-step solution. Suitable for students in Grades 8-10.

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