To rationalize the fraction [tex]\(\frac{15}{\sqrt{3}}\)[/tex], we need to eliminate the square root in the denominator. To do this, we multiply both the numerator and the denominator by the square root in the denominator, which is [tex]\(\sqrt{3}\)[/tex]. This process is known as rationalizing the denominator.
Here's the step-by-step procedure:
1. Start with the fraction:
[tex]\[
\frac{15}{\sqrt{3}}
\][/tex]
2. Multiply the numerator and the denominator by [tex]\(\sqrt{3}\)[/tex]:
[tex]\[
\frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}
\][/tex]
3. Perform the multiplication:
[tex]\[
\frac{15 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}
\][/tex]
4. Simplify the denominator, since [tex]\(\sqrt{3} \cdot \sqrt{3} = 3\)[/tex]:
[tex]\[
\frac{15 \cdot \sqrt{3}}{3}
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{15 \sqrt{3}}{3} = 5 \sqrt{3}
\][/tex]
Therefore, to rationalize the fraction [tex]\(\frac{15}{\sqrt{3}}\)[/tex], you multiply by [tex]\(\frac{\sqrt{3}}{\sqrt{3}}\)[/tex].
Looking at the given options:
A. [tex]\( 5 \)[/tex]
B. [tex]\( \frac{\sqrt{3}}{\sqrt{3}} \)[/tex]
C. [tex]\( \frac{\sqrt{5}}{\sqrt{5}} \)[/tex]
D. [tex]\( \frac{15}{\sqrt{3}} \)[/tex]
The correct answer is [tex]\( B. \frac{\sqrt{3}}{\sqrt{3}} \)[/tex].
