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

1 Answer

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