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

$22 \sqrt{- 1} = 22 i$

#### Explanation:

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

$2 \sqrt{- 4} + 3 \sqrt{- 36}$

$2 \sqrt{4 \times - 1} + 3 \sqrt{36 \times - 1}$

and from here we can do this:

$2 \sqrt{4} \sqrt{- 1} + 3 \sqrt{36} \sqrt{- 1}$

We can simplify the positive square roots as normal:

$2 \left(2\right) \sqrt{- 1} + 3 \left(6\right) \sqrt{- 1}$

$4 \sqrt{- 1} + 18 \sqrt{- 1}$

$22 \sqrt{- 1}$

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:

$22 i$