sqr(4) + 3^sqr(4) + 4^sqr(4) = 2 + 2^(2/3) + 2^(1/2)GHong14 wrote:
2^(2/3) = 2^(4/6) and 2^(1/2) = 2^(3/6)
2 + 2^(4/6) + 2^(3/6) = 2 + 2^(3/6)* (2^(1/6) + 1) = 2 + 2^(1/2)* (2^(1/6) +1) = approximately 2+ 1.41(1+1) is more than 4 but less than 6.
PS7
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Source: Beat The GMAT — Problem Solving |
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Night reader
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2^(2/3) = 2^(4/6) and 2^(1/2) = 2^(3/6)
2 + 2^(4/6) + 2^(3/6) = 2 + 2^(3/6)* (2^(1/6) + 1) = 2 + 2^(1/2)* (2^(1/6) +1) = approximately 2+ 1.41(1+1) is more than 4 but less than 6.
Last edited by Night reader on Mon Jan 10, 2011 8:50 pm, edited 1 time in total.
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anshumishra
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4^(1/2) = 2Night reader wrote:sqr(4)*(1+sqr(4)) +4^sqr(4)= 2*(1+2) +sqr(2)= 6+ sqr(2), hence greater than 4GHong14 wrote:
4^(1/4) = 2^(1/2) = 1.4
1.4 < 4^(1/3) < 4^(1/2)
So, 4^(1/2)+4^(1/3)+4^(1/4) > 2+1.4+1.4 > 4
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
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Night reader
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Anshu, I just revised solution it's less than 6 and more than 4. Thanks!anshumishra wrote:4^(1/2) = 2Night reader wrote:sqr(4)*(1+sqr(4)) +4^sqr(4)= 2*(1+2) +sqr(2)= 6+ sqr(2), hence greater than 4GHong14 wrote:
4^(1/4) = 2^(1/2) = 1.4
1.4 < 4^(1/3) < 4^(1/2)
So, 4^(1/2)+4^(1/3)+4^(1/4) > 2+1.4+1.4 > 4
