need help again: sqrt75a^2 / sqrt5

[pezgrl78]

sqrt75a^2 / sqrt5

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

can this be simplified? or am I correct?
Thanks

 

[jonboy]

Look at Skeeter's reply

 

[skeeter]

\(\displaystyle \L \frac{\sqrt{75a^2}}{\sqrt{5}} = \sqrt{\frac{75a^2}{5}} = \sqrt{15a^2} = |a| \cdot \sqrt{15}\)

 

[pezgrl78]

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

 

[daon]

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.

\(\displaystyle \L \frac{\sqrt{75a^2}}{\sqrt{5}} \,\, = \,\, \frac{\sqrt{75a^2}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} \,\, = \,\, \frac{\sqrt{375a^2}}{\sqrt{25}} \,\, \\ \,\, \,\, \,\, \,\, \,\, = \,\, \frac{\sqrt{25 \cdot 15 a^2}}{5} \,\, = \,\, \frac{\sqrt{(5a)^2 \cdot 15}}{5} \,\, \\ \,\, \,\, \,\, \,\, \,\, = \,\, \frac{|5a|\sqrt{15}}{5} \,\, = \,\, |a|\sqrt{15}\)

 

[jdruopp]

Just to let ya'll know I got the answer wrong. According to the teacher the correct answer is 5a.

 

[stapel]

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.

 

[jdruopp]

I didnt think so either but the question is posted correctly.