How do you simplify #sqrt2+3sqrt2#?

2 Answers

Answer:

#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#

Mar 7, 2018

Answer:

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)#