# How do you simplify sqrt2+3sqrt2?

$4 \sqrt{2}$

#### Explanation:

We can think of this in a couple of ways.

One way to approach this is to think of the $\sqrt{2}$ as a thing, like a ball. And so there is 1 ball and we're adding 3 more balls to the mix, so we have:

$1 \text{ ball" + 3 " balls"=4 " balls} \implies 4 \sqrt{2}$

Another way to think of this is to remember that if we multiply anything by 1, we don't change the value of the number. So I can say:

$\sqrt{2} + 3 \sqrt{2} = 1 \sqrt{2} + 3 \sqrt{2}$

I can now factor out the $\sqrt{2}$:

$1 \sqrt{2} + 3 \sqrt{2} = \sqrt{2} \left(1 + 3\right) = \sqrt{2} \left(4\right)$

and then reorder the terms:

$\sqrt{2} \left(4\right) = 4 \sqrt{2}$

Mar 7, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\textcolor{red}{1} \sqrt{2} + 3 \sqrt{2}$

Now factor out the common term of $\sqrt{2}$ and simplify:

$\left(\textcolor{red}{1} + 3\right) \sqrt{2} \implies$

$4 \sqrt{2}$