# How do you simplify 5sqrt(-75) - 9sqrt(-300)?

Jan 27, 2016

You use the rule $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$- 65 \sqrt{3} i$

Note DON'T fall into the trap of simplifying the minus signs of the roots with the outer signs.

#### Explanation:

$5 \sqrt{- 75} - 9 \sqrt{- 300}$

$5 \sqrt{- 3 \cdot 2} - 9 \sqrt{- 3 \cdot 100}$

$5 \sqrt{- 3} \cdot \sqrt{25} - 9 \sqrt{- 3} \cdot \sqrt{100}$

$5 \cdot 5 \cdot \sqrt{- 3} - 9 \sqrt{- 3} \cdot 10$

$25 \cdot \sqrt{- 3} - 90 \sqrt{- 3}$

$i 25 \cdot \sqrt{3} - i 90 \sqrt{3}$

$i \sqrt{3} \cdot \left(25 - 90\right)$

$- 65 \sqrt{3} i$