SOLUTION: How does: 1/24*(24/5)^(1/2) = (1/(24*5))^(1/2) which comes to (1/120)^(1/2) This seems quite easy yet I can't figure it out. I did find that if I square 1/24 I get 1/576

Algebra ->  Square-cubic-other-roots -> SOLUTION: How does: 1/24*(24/5)^(1/2) = (1/(24*5))^(1/2) which comes to (1/120)^(1/2) This seems quite easy yet I can't figure it out. I did find that if I square 1/24 I get 1/576       Log On


   

Question 1016400: How does:
1/24*(24/5)^(1/2) = (1/(24*5))^(1/2)
which comes to (1/120)^(1/2)
This seems quite easy yet I can't figure it out.
I did find that if I square 1/24 I get 1/576 and if I square the root I get 24/5.
Then I found this 1/576*24/5 cancels down to 1/120. However the answer in the book is (1/120)^(1/2).
If anyone could help with this I would really appreciate it.
Thank you in advance.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
To start: 1%2F24=sqrt%281%2F24%5E2%29
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%281%2F24%29%2A%2824%2F5%29%5E%281%2F2%29+=+%281%2F%2824%2A5%29%29%5E%281%2F2%29
.
%281%2F24%29sqrt%2824%2F5%29=sqrt%281%2F%2824%2A5%29%29
.
sqrt%281%2F24%5E2%29sqrt%2824%2F5%29=sqrt%281%2F%2824%2A5%29%29
.
sqrt%28%281%2F24%5E2%29%2824%2F5%29%29=sqrt%281%2F%2824%2A5%29%29
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sqrt%2824%2F%2824%5E2%2A5%29%29=sqrt%281%2F%2824%2A5%29%29
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sqrt%281%2F%2824%2A5%29%29=sqrt%281%2F%2824%2A5%29%29
.