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...

Asked on by nasirjam

1 Answer | Add Yours

degeneratecircle's profile pic

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted on

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.

We’ve answered 319,816 questions. We can answer yours, too.

Ask a question