Question

Divide
36sqrt39
-. Provide an exact answer. (1 point)
9sqrt13

Answer 1

Simplify sqrt48. (1 point)

Answer 2

To divide \( 36\sqrt{39} \) by \( 9\sqrt{13} \), we follow these steps:

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

First, we can simplify the coefficients (the numbers outside the square roots):

\[
\frac{36}{9} = 4
\]

Next, we can rewrite the expression:

\[
\frac{36\sqrt{39}}{9\sqrt{13}} = 4 \cdot \frac{\sqrt{39}}{\sqrt{13}}
\]

Now, we can simplify \( \frac{\sqrt{39}}{\sqrt{13}} \) as follows:

\[
\frac{\sqrt{39}}{\sqrt{13}} = \sqrt{\frac{39}{13}} = \sqrt{3}
\]

Now we can combine the results:

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

Thus, the exact answer is:

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

Answer 3

To simplify \(\sqrt{48}\), we can start by factoring \(48\) into its prime factors:

\[
48 = 16 \times 3
\]

Next, we can take the square root of \(16\) since it's a perfect square:

\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]

Thus, the simplified form of \(\sqrt{48}\) is:

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