need help again: sqrt75a^2 / sqrt5

pezgrl78

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Joined
Apr 27, 2007
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14
sqrt75a^2 / sqrt5

I get an answer of (5a)sqrt3 / 5

can this be simplified? or am I correct?
Thanks
 
\(\displaystyle \L \frac{\sqrt{75a^2}}{\sqrt{5}} = \sqrt{\frac{75a^2}{5}} = \sqrt{15a^2} = |a| \cdot \sqrt{15}\)
 
Thanks.

I thought I had to multiply top and bottom by sqrt5 to rationalize the denominator. I didnt know I could just divide 75 by 5.
Thanks
 
pezgrl78 said:
Thanks.

I thought I had to multiply top and bottom by sqrt5 to rationalize the denominator. I didnt know I could just divide 75 by 5.
Thanks

Either way works fine.

\(\displaystyle \L \frac{\sqrt{75a^2}}{\sqrt{5}} \,\, = \,\, \frac{\sqrt{75a^2}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} \,\, = \,\, \frac{\sqrt{375a^2}}{\sqrt{25}} \,\, \\ \,\, \,\, \,\, \,\, \,\, = \,\, \frac{\sqrt{25 \cdot 15 a^2}}{5} \,\, = \,\, \frac{\sqrt{(5a)^2 \cdot 15}}{5} \,\, \\ \,\, \,\, \,\, \,\, \,\, = \,\, \frac{|5a|\sqrt{15}}{5} \,\, = \,\, |a|\sqrt{15}\)
 
Just to let ya'll know I got the answer wrong. According to the teacher the correct answer is 5a.
 
jdruopp said:
According to the teacher the correct answer is 5a.
Only if the expression was posted incorrectly, because there is no way to get "5a" from "sqrt[75a^2] / sqrt[5]". Sorry.

Eliz.
 
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