Question

How do you simplify `sqrt2+3sqrt2`?

Answer 1

`4sqrt2`

Explanation:

We can think of this in a couple of ways.

One way to approach this is to think of the `sqrt2` 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 " ball" + 3 " balls"=4 " balls"=>4sqrt2`

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:

`sqrt2+3sqrt2=1sqrt2+3sqrt2`

I can now factor out the `sqrt2`:

`1sqrt2+3sqrt2=sqrt2(1+3)=sqrt2(4)`

and then reorder the terms:

`sqrt2(4)=4sqrt2`

Answer 2

See a solution process below:

Explanation:

First, rewrite the expression as:

`color(red)(1)sqrt(2) + 3sqrt(2)`

Now factor out the common term of `sqrt(2)` and simplify:

`(color(red)(1) + 3)sqrt(2) =>`

`4sqrt(2)`