It Works For Any Positive Number?

Calculus Level 1

Take any positive number.
Add 20, then take the square root of the result.
Add 20, then take the square root of the result again.
Add 20, then take the square root of the result again.

If you continued doing this, what value would the results converge to?

4 5 6 7

2 solutions

Alex G
Apr 20, 2016

Relevant wiki: Nested Functions

The problem is just a fancy way of posing an infinite nested radical.

Writing out the stated radical:

$\sqrt{\sqrt{\sqrt{x+20}+20}+...+20}$

Let $L$ equal the nested radical.

$L^2= \sqrt{\sqrt{\sqrt{x+20}+20}+...+20}+20$

$L^2= L+20$

$L^2 -L +20 =0$

$(L-5)(L+4)=0$

Note that the square root is defined as the positive value, therefore $L= \boxed{5}$

Yeah...kind of lame and not cool at dinner parties. But neat!

Chris Stringer - 5 years, 1 month ago

Admittingly, this is the kind of thing I'd bring up at a dinner party. "Alright folks! Who here has a pen and paper?"

Andrew Tawfeek - 5 years, 1 month ago

Nitish Songara
Jul 4, 2016

Bebecoz user will select any but after listening of sqrt they change their mind and try to make things easy

It Works For Any Positive Number?

2 solutions

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