Without a calculator: Which is greater √(5+5√5) or 4?
Without a calculator: Which is greater √(7+7√7) or 5?
PART A
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V5 = 2* (5/4)^(1/2)
= 2*(1 +1/4)^(1/2)
= 2(1+ 1/8- 1/64+.....) --> expanding in terms of Binomial Theorem.
> 2(1+1/8-1/64) = 2*(1+ 7/64) = 2+ 7/32 = 71/32
Then, we must have:
5+5V5 > 5+ 5*(71/32) = (160+355)/32= 515/32 > 512/32 =16
Consequently, V(5+5V5) > V16 = 4
Calculator corroboration has been done in Method - 1, and so it is not repeated here.
Edited on June 3, 2022, 7:51 am
Puzzle Solution : Part A : Method 2
