Problem 957

Express in terms of i.

$\sqrt{-9} + \sqrt{-20}$

Solution:-

First, factor the radicands using perfect square factors.

$\sqrt{-9}+\sqrt{-20} = \sqrt{-1(9)}+\sqrt{-1(4)(5)}$

Next , factor into several radicals.

$\sqrt{(-1)9}+\sqrt{-1(4)(5)} = \sqrt{-1(9)}+\sqrt{-1(4)(5)}$

Now, simplify each radical if possible.

$\sqrt{(-1)9}+\sqrt{-1(4)(5)} = i3 + i2\sqrt{5}$

Finally , factor out the common factor i.

$i3 + i2\sqrt{5}=(3+2\sqrt{5})i$

$\sqrt{-9}+\sqrt{-20}=(3+2\sqrt{5})i$