How do you simplify #2sqrt(-4) + 3sqrt(-36)#?

1 Answer
MathFact-orials.blogspot.com
Jul 1, 2018

#22sqrt(-1)=22i#

Explanation:

Notice that we can break down the terms inside the square root signs into positive numbers and #-1#:

#2sqrt(-4)+3sqrt(-36)#

#2sqrt(4xx-1)+3sqrt(36xx-1)#

and from here we can do this:

#2sqrt4sqrt(-1)+3sqrt36sqrt(-1)#

We can simplify the positive square roots as normal:

#2(2)sqrt(-1)+3(6)sqrt(-1)#

#4sqrt(-1)+18sqrt(-1)#

#22sqrt(-1)#

And here's one place we can stop; the #sqrt(-1)# makes the terms imaginary. If you like, we can replace #sqrt(-1)# with the term #i# (mathematicians use #i# to make imaginary numbers easier to write). And so we can also write:

#22i#

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