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Since the answer choices are dissimilar, we can estimate the answer choice here. The \(\sqrt[2]{20}\) is somewhere between 4 and 5. Suppose it's 5, then we'll get \(\sqrt[2]{20+\sqrt[2]{20+5}\)=\(\sqrt[2]{20+5}\)=\(5\)

2: From third sqrt: sqrt 20 = 4 and a fraction of 1. From second sqrt: sqrt (20+4.00 = 24) = 4 and a fraction of 1. From first sqrt: sqrt (20+4.00 = 24) = 4 and a fraction of 1. which is definitely close to none other than 5.

3: Using POE:

A: it cannot be 20 cuz for 20, the value under root must be 400, which is impossible. so A is ruled out. B: It could be 5 as done above in method 2. 3. 2 is also not possible because even if we consider first 20 under root, the value must not be smaller than 4. 4. 8 is not possible because for 8, the value under root must be 64. Even if we add up all three 20s, the sum would not be more than 60. so it is also not possible. So left with 5.

Bunuel, would you be so kind and look at this question. Is there any other way to solve it rather than elimination? Can you describe elimination in greater detail? Thank you.

Bunuel, would you be so kind and look at this question. Is there any other way to solve it rather than elimination? Can you describe elimination in greater detail? Thank you.

Find the value of x

\(x= \sqrt{20+\sqrt{20+\sqrt{20}}}\)

1. 20 2. 5 3. 2 4. 8

Question should be what is the approximate value of \(x\).

Obviously answer choice C (2) is out as \(\sqrt{20+some \ #}>4\).

Now, \(4<\sqrt{20}<5\): \(x= \sqrt{20+\sqrt{20+\sqrt{20}}}= \sqrt{20+\sqrt{20+(# \ less \ than \ 5)}}= \sqrt{20+\sqrt{# \ less \ than \ 25}}= \sqrt{20+(# \ less \ than \ 5)}=\)

\(=\sqrt{# \ less \ than \ 25}=# \ less \ than \ 5\approx{5}\).

Answer: B.

Next, exactly 5 to be the correct answer question should be:

If the expression \(x=\sqrt{20+{\sqrt{20+\sqrt{20+\sqrt{20+...}}}}}\) extends to an infinite number of roots and converges to a positive number x, what is x?

\(x=\sqrt{20+{\sqrt{20+\sqrt{20+\sqrt{20+...}}}}}\) --> \(x=\sqrt{20+({\sqrt{20+\sqrt{20+\sqrt{20+...})}}}}\), as the expression under square root extends infinitely, then expression in brackets would equal to \(x\) itself so we can rewrite given expression as \(x=\sqrt{20+x}\). Square both sides \(x^2=20+x\) --> \(x=5\) or \(x=-4\). As given that \(x>0\) then only one solution is valid: \(x=5\).

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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why is it that only 4 options given in the question? I think that this is not a gmat type question as for explanation,I agree with bunuel that it needs to be asking approximate value of x Correct Ans - B

Fortunately there is a super short cut to solve this question (that shortcut is applicable to this question atleast ) This whole expression can be seen as \(x= \sqrt[2]{20+\sqrt[2]{some number}\)

. Square root of 20 is 4.4 approx and the rest of the nested square root will be a small decimal value because they are square root inside square root

so the answer will be 4.4 + 0.some value

Look out for a nearest answer greater than 4.4

It's 5 in the given question

SO the answer is B

If you get this kind of questions in GMAT , thank your stars because you can save tremendous amount of time and add sure marks to your score.

ritula wrote:

Find the value of x

\(x= \sqrt[2]{20+\sqrt[2]{20+\sqrt[2]{20}}}\)

1. 20 2. 5 3. 2 4. 8

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

gmatclubot

Re: Find the value of x
[#permalink]
08 Jul 2016, 22:06

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