To simplify the expression \(\frac{\sqrt{720}}{\sqrt{9}}\), we can start by simplifying both square roots separately.
First, we know that: \[ \sqrt{9} = 3 \]
Now, let's simplify \(\sqrt{720}\). We can factor \(720\) to make it easier to take the square root: \[ 720 = 72 \times 10 \] Further breaking down \(72\) gives us: \[ 72 = 36 \times 2 = 6^2 \times 2 \] And \(10\) can be factored as: \[ 10 = 2 \times 5 \]
Putting it all together, we have: \[ 720 = (6^2 \times 2) \times (2 \times 5) = 6^2 \times 2^2 \times 5 \] Now, we can use this to simplify \(\sqrt{720}\): \[ \sqrt{720} = \sqrt{6^2 \times 2^2 \times 5} = 6 \times 2 \times \sqrt{5} = 12\sqrt{5} \]
Now, substituting back into our original expression gives: \[ \frac{\sqrt{720}}{\sqrt{9}} = \frac{12\sqrt{5}}{3} \]
Dividing \(12\) by \(3\) gives us: \[ \frac{12}{3} = 4 \] Thus, the expression simplifies to: \[ \frac{\sqrt{720}}{\sqrt{9}} = 4\sqrt{5} \]
So, the expression in simplest radical form is: \[ \boxed{4\sqrt{5}} \]