# How do you multiply 5sqrt(8)(2sqrt(18)+3sqrt(10)?

##### 1 Answer
Feb 5, 2015

First remember that what is outside the radical is multiplied together and what is inside the radical is multiplied together.

We will start off by distributing the $5 \sqrt{8}$

$5 \sqrt{8} \left(2 \sqrt{18}\right) + 5 \sqrt{8} \left(3 \sqrt{10}\right)$

When we actually multiply these do not write out the product of the numbers under the radical. We will need to factor these later.

$10 \sqrt{8 \cdot 18} + 15 \sqrt{8 \cdot 10}$

We now need to do a prime factorization of what is under the radical.

$10 \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3} + 15 \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 5}$

When taking the square root, we are looking for "two of a kind".
In the first radical we have two pairs of 2s and one pair of 3s.

In the second radical we have two pairs of 2s. The 5 will remain under the radical since it is not a pair.

$10 \cdot 2 \cdot 2 \cdot 3 + 15 \cdot 2 \cdot 2 \sqrt{5}$
$120 + 60 \sqrt{5}$