Question

Express in simplest radical form.
start fraction, square root of, 720, end square root, divided by, square root of, 9, end square root, end fraction
9
​

720
​

​

Answer
Attempt 1 out of 5

Submit Answer
square root of, end square root
x
​

Answer 1

To simplify the expression \(\frac{\sqrt{720}}{\sqrt{9}}\), we can start by simplifying each square root separately.

\[
\sqrt{9} = 3
\]

Next, we simplify \(\sqrt{720}\).

The prime factorization of \(720\) is:
\[
720 = 2^4 \times 3^2 \times 5
\]

Now, we can take the square root:
\[
\sqrt{720} = \sqrt{2^4 \times 3^2 \times 5} = \sqrt{2^4} \times \sqrt{3^2} \times \sqrt{5} = 2^2 \times 3 \times \sqrt{5} = 4 \times 3 \times \sqrt{5} = 12\sqrt{5}
\]

Now substitute back into the original expression:
\[
\frac{\sqrt{720}}{\sqrt{9}} = \frac{12\sqrt{5}}{3}
\]

Now simplify:
\[
\frac{12\sqrt{5}}{3} = 4\sqrt{5}
\]

Thus, the expression in simplest radical form is:
\[
\boxed{4\sqrt{5}}
\]