# How do you evaluate 3√12 +4√18?

Apr 7, 2018

$6 \sqrt{3} + 12 \sqrt{2}$

#### Explanation:

The only way to simplify radicals is to take the radicand (the number under the radical) and split it into two factors, where one of them has to be a $\text{perfect square}$

A $\text{perfect square}$ is a product of two of the same numbers

Example: $9$ is a $\text{perfect square}$ because $3 \cdot 3 = 9$

So, let's simplify and pull some numbers out of these radicals:

$3 \sqrt{12} + 4 \sqrt{18}$ color(blue)(" Let's start with the left side"
$3 \sqrt{4 \cdot 3} + 4 \sqrt{18}$ $\textcolor{b l u e}{\text{ 4 is a perfect square}}$
$3 \cdot 2 \sqrt{3} + 4 \sqrt{18}$ $\textcolor{b l u e}{\text{ 4 is a perfect square, so take a 2 out}}$
$6 \sqrt{3} + 4 \sqrt{18}$ $\textcolor{b l u e}{\text{ Simplify: "3*2=6," and leave the 3}}$
$6 \sqrt{3} + 4 \sqrt{9 \cdot 2}$ $\textcolor{b l u e}{\text{ 9 is a perfect square}}$
$6 \sqrt{3} + 4 \cdot 3 \sqrt{2}$ $\textcolor{b l u e}{\text{ 9 is a perfect square, so take a 3 out}}$
$6 \sqrt{3} + 12 \sqrt{2}$ $\textcolor{b l u e}{\text{ Simplify: "4*3=12," and leave the 2}}$
$\textcolor{red}{6 \sqrt{3} + 12 \sqrt{2}}$

Since $\sqrt{3}$ and $\sqrt{2}$ are different radicals, we can't add them, so we're done.