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quick comparison

by ramyaravindran » Tue Mar 09, 2010 12:02 pm
This may be a simple concept but it is eluding me now. How can you quickly estimate if sqrt(78*79*80*81) is greater than or less than 6400?
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by dtweah » Tue Mar 09, 2010 1:46 pm
ramyaravindran wrote:This may be a simple concept but it is eluding me now. How can you quickly estimate if sqrt(78*79*80*81) is greater than or less than 6400?
(Root( 78, 79, 80, 81) )^2


(80 80 )^2

78 78 80 81


80 80 80 80
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by kevincanspain » Tue Mar 09, 2010 2:09 pm
ramyaravindran wrote:This may be a simple concept but it is eluding me now. How can you quickly estimate if sqrt(78*79*80*81) is greater than or less than 6400?
Remember that 81^2 * 79^2 =(80^2 - 1^2)^2 < 80^4

Alternatively, 81 x 79 =80^2 - 1^2 < 80^2

80 x 78 < 80^2
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by happyzzim » Tue Mar 09, 2010 2:34 pm
Q. sqrt(78*79*80*81) is greater than or less than 6400?

A. sqrt(78*79*80*81) < sqrt(79*79*81*81) = sqrt(79^2*81^2) = 6399 < 6400

For the reason, sqrt(78*79*80*81) < 6400
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