preform the indicated operation. be sure to rationalize the denominator when necessary.make sure to simplify as much as possible and givw the exact answer (this means NO decimals since decimals is rounding!)

Question

15/7square root of 3

Answer 1

To rationalize the denominator of the expression \(\frac{15}{7 \sqrt{3}}\), we will multiply both the numerator and denominator by \(\sqrt{3}\):

\[ \frac{15}{7 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{15 \sqrt{3}}{7 \cdot 3} \]

Now, simplify the denominator:

\[ 7 \cdot 3 = 21 \]

Thus, the expression becomes:

\[ \frac{15 \sqrt{3}}{21} \]

Next, we can simplify this further by dividing both the numerator and denominator by their greatest common divisor, which is 3:

\[ \frac{15 \div 3}{21 \div 3} = \frac{5 \sqrt{3}}{7} \]

Therefore, the final answer is:

\[ \frac{5 \sqrt{3}}{7} \]