To rationalize the denominator of the fraction [tex]\(\frac{5}{\sqrt{15}}\)[/tex], follow these steps:
1. Identify the fraction and the irrational denominator:
- The given fraction is [tex]\(\frac{5}{\sqrt{15}}\)[/tex].
2. Multiply both the numerator and the denominator by the radical in the denominator:
- Here, we multiply both the numerator and the denominator by [tex]\(\sqrt{15}\)[/tex].
- This gives us:
[tex]\[
\frac{5}{\sqrt{15}} \times \frac{\sqrt{15}}{\sqrt{15}}
\][/tex]
3. Simplify the expression:
- The numerator becomes:
[tex]\[
5 \times \sqrt{15} = 5\sqrt{15}
\][/tex]
- The denominator becomes:
[tex]\[
\sqrt{15} \times \sqrt{15} = 15
\][/tex]
4. Form the new fraction with the rationalized denominator:
- The new fraction is:
[tex]\[
\frac{5\sqrt{15}}{15}
\][/tex]
Therefore, the rationalized form of the fraction [tex]\(\frac{5}{\sqrt{15}}\)[/tex] is [tex]\(\frac{5\sqrt{15}}{15}\)[/tex].
Upon evaluating this expression numerically, the numerator approximately equals 19.364916731037084 and the denominator is 15.
So, the final rationalized form is:
[tex]\[
\frac{19.364916731037084}{15}
\][/tex]
