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Which is Largest?

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Master | Next Rank: 500 Posts
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by dtweah » Wed May 06, 2009 6:59 am
Which of the Following is largest?
A. 2^1/2

B. 5^1/3

C. 8^1/4

D. 11^1/5

E. 14^1/6
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by abhinav85 » Wed May 06, 2009 7:01 am
i think A

what is OA?
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by mikeCoolBoy » Wed May 06, 2009 7:32 am
I got B

here is what I did

first comparison

2^1/2 > 14^1/6? ---> (2^1/2)^6 > (14^1/6)^6 ---> 2^3 > 14 not true so 14^1/6 > 2^1/2

second comparison

14^1/6 < 5^1/3 ? ---> (14^1/6)^6 < (5^1/3)^6 ---> 14 < 25 true so 5^1/3 > 14^1/6

third comparison

8^1/4 > 5^1/3? ----> (8^1/4) ^12 > (5^1/3)^12 ---> 8^3 > 5 ^4 not true so 5^1/3 > 8^1/4

last comparison

11^1/5 > 5^1/3? ---> (11^1/5)^15 > (5^1/3)^15 ---> 11^3 > 5^5 not true so 5^1/3 is the largest
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by dtweah » Wed May 06, 2009 10:23 am
mikeCoolBoy wrote:I got B

here is what I did

first comparison

2^1/2 > 14^1/6? ---> (2^1/2)^6 > (14^1/6)^6 ---> 2^3 > 14 not true so 14^1/6 > 2^1/2

second comparison

14^1/6 < 5^1/3 ? ---> (14^1/6)^6 < (5^1/3)^6 ---> 14 < 25 true so 5^1/3 > 14^1/6

third comparison

8^1/4 > 5^1/3? ----> (8^1/4) ^12 > (5^1/3)^12 ---> 8^3 > 5 ^4 not true so 5^1/3 > 8^1/4

last comparison

11^1/5 > 5^1/3? ---> (11^1/5)^15 > (5^1/3)^15 ---> 11^3 > 5^5 not true so 5^1/3 is the largest
Cool explanation. The way to attack it.
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by criszerriny » Wed May 06, 2009 7:35 pm
That was awesome!
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