Without a calculator: Which is greater √(5+5√5) or 4?
Without a calculator: Which is greater √(7+7√7) or 5?
PART B
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V7 = (V28)/2
= (5/2)*V(1+3/25)
Now, (1+3/25)^(1/2)
= 1+3/50 -9/2500+....
> (1+3/50-9/2500)
= 1+ 141/2500
Accordingly,
V7 > (5/2)*(1+141/2500)
= 2.5 + 0.141
= 2.641
Therefore:
7+7V7 > 7+7*2.641
= 7+18.487
=25.487
>25
So, V(7+7V7) > V25 = 5
Consequently, V(7+7V7) is the greater quantity.
**** Calculator corroboration has already been shown in Method 1, so it is not presented here.
Edited on June 3, 2022, 7:50 am
Puzzle Solution: Part B : Method 2
