To solve the question regarding whether to rationalize the denominator that has more than one term, you multiply the fraction by [tex]\(\frac{B}{B}\)[/tex], where [tex]\(B\)[/tex] is the conjugate of the numerator, follow these steps:
1. Understanding the Conjugate:
- The conjugate of a binomial expression [tex]\(a + b\)[/tex] is [tex]\(a - b\)[/tex], and the conjugate of [tex]\(a - b\)[/tex] is [tex]\(a + b\)[/tex].
- Conjugates are used in rationalizing denominators to eliminate radicals.
2. Rationalizing the Denominator:
- When rationalizing a denominator with more than one term (a binomial), you should multiply both the numerator and the denominator by the conjugate of the denominator, not the numerator.
- This method uses the difference of squares [tex]\( (a + b)(a - b) = a^2 - b^2 \)[/tex] to eliminate the radical or binomial in the denominator.
3. Example to illustrate:
- Suppose you have a fraction like [tex]\(\frac{3}{2 + \sqrt{5}}\)[/tex].
- To rationalize the denominator, you multiply both the numerator and the denominator by the conjugate of the denominator, which is [tex]\(2 - \sqrt{5}\)[/tex].
Hence, the fraction becomes:
[tex]\[
\frac{3}{2 + \sqrt{5}} \cdot \frac{2 - \sqrt{5}}{2 - \sqrt{5}} = \frac{3(2 - \sqrt{5})}{(2 + \sqrt{5})(2 - \sqrt{5})}
\][/tex]
Simplifying the denominator:
[tex]\[
(2 + \sqrt{5})(2 - \sqrt{5}) = 4 - 5 = -1
\][/tex]
So the fraction becomes:
[tex]\[
\frac{3(2 - \sqrt{5})}{-1} = -3(2 - \sqrt{5})
\][/tex]
In conclusion, to rationalize a denominator that has more than one term, you multiply the fraction by [tex]\(\frac{B}{B}\)[/tex] where [tex]\(B\)[/tex] is the conjugate of the denominator, not the numerator. Therefore, the correct answer is:
B. False
