How do you simplify $5 \sqrt{- 75} - 9 \sqrt{- 300}$ $5sqrt(-75) - 9sqrt(-300)$ ?

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Answer 1 · 2016-01-27T09:59:05

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

$- 65 \sqrt{3} i$ $-65sqrt(3)i$

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

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

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

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

$5 \cdot 5 \cdot \sqrt{- 3} - 9 \sqrt{- 3} \cdot 10$ $5*5*sqrt(-3)-9sqrt(-3)*10$

$25 \cdot \sqrt{- 3} - 90 \sqrt{- 3}$ $25*sqrt(-3)-90sqrt(-3)$

$i 25 \cdot \sqrt{3} - i 90 \sqrt{3}$ $i25*sqrt(3)-i90sqrt(3)$

$i \sqrt{3} \cdot (25 - 90)$ $isqrt(3)*(25-90)$

$- 65 \sqrt{3} i$ $-65sqrt(3)i$

How do you simplify 5√−75−9√−3005sqrt(-75) - 9sqrt(-300)?