Find the value of `sqrt(5 + sqrt(11 + sqrt(19 + sqrt(20 +sqrt(49)))))` .a. 3b. 5c. 16d. 46This is a very a good question and let's see who solves it...
It's not any of those. According to my computer, it's approximately 2.998309, which is very close to 3, but it's not exact.
For it to be 3, `sqrt(11+sqrt(19+sqrt(27)))` would have to be 4, and so
`sqrt(19+sqrt(27))` would have to be 5, and `19+sqrt(27)` is not 25 because `sqrt(27)` is irrational, and since `sqrt(27)<6,` `19+sqrt(27)<25,` and this also proves that the answer is less than 3, eliminating all the other choices.