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Find the value of `sqrt(5 + sqrt(11 + sqrt(19 + sqrt(20 +sqrt(49)))))` .a. 3b. 5c. 16d....

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nasirjam | Student, Grade 9 | Honors

Posted March 1, 2013 at 10:17 PM via web

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Find the value of `sqrt(5 + sqrt(11 + sqrt(19 + sqrt(20 +sqrt(49)))))` .
a. 3
b. 5
c. 16
d. 46

This is a very a good question and let's see who solves it...

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

Posted March 2, 2013 at 4:47 AM (Answer #1)

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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.

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