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Simplify the expression . Show your work.

oscar.a1551  Oct 1, 2018
 #1
avatar+991 
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Answer:

GAMEMASTERX40  Oct 1, 2018
 #2
avatar+94100 
+2

Thanks gamesmaster

\(\sqrt{x^2}=|x| \qquad not\;\;x\)

 

If this expression is real then y must be positive.   

Also if an expression is simple then the denominator should be rational. (no Square root on the bottom)

Although your teacher may not care about this.\(\)

 

\(\sqrt\frac{4x^2}{3y}\\=\frac{|2x|}{\sqrt{3y}}\\ =\frac{|2x|}{\sqrt{3y}}\times \frac{\sqrt{3y}}{\sqrt{3y}}\\ =\frac{|2x|\sqrt{3y}}{3y} \\ =\left| \frac{2x\sqrt{3y}}{3y} \right|\\~\\ = \frac{2x\sqrt{3y}}{3y} \text{ when }x\ge0\\ = \frac{-2x\sqrt{3y}}{3y} \text{ when }x<0\)

Melody  Oct 2, 2018

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