Answer
$24 \sqrt{5}$
Work Step by Step
First of all, in order to make this one large square root, we multiply the coefficients to obtain that the new coefficient is 8. Also, recall, $\sqrt{a}\times \sqrt{b}= \sqrt{a \times b}$. Thus, we can multiply 3 and 15 to obtain the simplified expression:
$8\sqrt{3 \times 15}=8\sqrt{45}$
In order to simplify a radical, we consider the factors of the number inside of the radical. If any of these factors are perfect squares, meaning that their square root is a whole number, then we can simplify the radical. We know that 9 and 5 are factors of 45. We know that 9 is a perfect square, so we simplify:
$8 \sqrt{9} \sqrt{5}=24 \sqrt{5}$
