Bunuel wrote:
conty911 wrote:
Find the value of a. Given a=√3(√3(√3(√3(√3…….inf.))))..
[PS: nested sq. root sequence is repeated infinite times.]A. 0
B. \(\sqrt{3}\)
C. 3
D. 2.9
E. cannot be determined.
a=√3(√3(√3(√3(√3…….inf.))))
sq. both sides
a^2=3(√3(√3(√3(√3(√3…….inf.)))))
or
a^2=3a ; since, a=√3(√3(√3(√3(√3…….inf.))))
a^2-3a=0
a(a-3)=0
a=0/3
0 logically doesn't fit so 3 is the ans
Interesting question.
Mods, if the question needs reformatting please do so, as i was not able to properly use the sqrt symbol, given in the editor.
Added a pic, pls pardon my drawing
For those who are confused by formatting:
If \(a=\sqrt{3\sqrt{3\sqrt{3\sqrt{3...}}}}\), what is the value of a?A. 0
B. \(\sqrt{3}\)
C. 3
D. 2.9
E. cannot be determined.
\(a=\sqrt{3\sqrt{3\sqrt{3\sqrt{3...}}}}\) --> \(a=\sqrt{3(\sqrt{3\sqrt{3\sqrt{3...}}})}\). Now, as the expression under the square root extends infinitely, then expression in brackets would equal to \(a\) itself, so we can safely replace it with \(a\) and rewrite the given expression as \(a=\sqrt{3a}\).
Square it: \(a^2=3a\) --> \(a=0\) or \(a=3\) --> since \(a=0\) does not satisfy given expression, then we have only one solution: \(a=3\).
Answer: C.
Another genius explanation from
Bunuel, Kudos to you
I had in mind that \(\sqrt{3} = 1.732\) To square root it multiple times will give the value 1.00000000000xxxxxxxxxxx & so on
Now that 1 is not the option in the OA, nearest to it was 0, which I selected & went wrong
Bunuel, can you kindly explain
I opened the scientific calculator & square rooted 3 multiple times, which stuck at 1
Attachment:
calc.png [ 17.3 KiB | Viewed 47291 times ]
Now had 1 been in the OA, which would had been the answer?
(I agree that answer = 3, however the result 1 from calculator is contradicting)