Divide 36√39 9√13

Question

. Provide an exact answer. (1 point)

Answer 1

To divide \( 36\sqrt{39} \) by \( 9\sqrt{13} \), we can write the expression as follows:

\[ \frac{36\sqrt{39}}{9\sqrt{13}} \]

Now, we can simplify the fraction step by step:

1. Divide the coefficients: \[ \frac{36}{9} = 4 \]

2. Write down the square roots: \[ \sqrt{39} \text{ and } \sqrt{13} \]

So, we can rewrite the expression as:

\[ 4 \cdot \frac{\sqrt{39}}{\sqrt{13}} \]

3. Simplify the square roots: \[ \frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3} \]

Thus, putting everything together, we have:

\[ 4\sqrt{3} \]

Therefore, the exact answer is:

\[ \boxed{4\sqrt{3}} \]