Problem 957

Express in terms of i.

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




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



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