# A rope is sqrt 250 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 3:2 . What is the length of the longer piece expressed in simplest radical form?

$3 \sqrt{10}$
You can simplify $\sqrt{250}$ to $5 \sqrt{10}$. Then, you know that each "part" in the ratio is equivalent to $\sqrt{10}$. Then, by logic, you know that the longer piece is the part with a ratio equivalent to 3. Now, all you have to do is multiply $\sqrt{10}$ by 3 to get $3 \sqrt{10}$, which is simplified.