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Magoosh GMAT Instructor
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Rank those three in order from smallest to biggest. [#permalink]
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27 Sep 2016, 17:20
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61% (01:06) correct 39% (01:01) wrong based on 129 sessions
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Rank those three in order from smallest to biggest.
(A) I, II, III (B) I, III, II (C) II, I, III (D) II, III, I (E) III, II, IThis problem involves a bit of number sense. For a discussion of this skill, as well as the OE for this particular question, see: Number Sense for the GMATMike
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Re: Rank those three in order from smallest to biggest. [#permalink]
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27 Sep 2016, 18:45
We can write all the terms with the same exponent \(\sqrt{5}\) , \(\sqrt[3]{2}\), \(\sqrt[4]{401}\) \(\sqrt[3]{5^6}\), \(\sqrt[3]{2^4}\), \(\sqrt[4]{401^3}\)
We know \(2^4\) < \(5^6\), so II < I
\(5^6\) = \(125^3\) <\(401^3\) So I < III
II < I < III Option C



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Re: Rank those three in order from smallest to biggest. [#permalink]
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27 Sep 2016, 19:44
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mikemcgarry wrote: Attachment: three roots.png Rank those three in order from smallest to biggest. (A) I, II, III (B) I, III, II (C) II, I, III (D) II, III, I (E) III, II, IThis problem involves a bit of number sense. For a discussion of this skill, as well as the OE for this particular question, see: Number Sense for the GMATMike Get them in same roots.. I. 2√5= √(2*2*5)=√20= 4th root of 20*20 or 4th root of 400 II. 3√2=√3*3*2=√18  so LESS than I Let's check III now III. 4th root of 401 so GREATER than I.. therefore the greatest So smallest to largest  II, I, III C
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Re: Rank those three in order from smallest to biggest. [#permalink]
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27 Sep 2016, 20:55
for expressions like this we need to take lcm of the roots of the expressions
on taking lcm, these terms can be written as 5^6 , 2^4, 401^3
now its clear which one is smallest and which one is biggest term
2^4 < 5^6 < 401^3
Option C



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Re: Rank those three in order from smallest to biggest. [#permalink]
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24 Dec 2017, 07:02
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Raising the power of all the options to power 4, will help rank easily
1. \((2 * \sqrt{5})^4\) = \(2^4 * 5^2\) = 400 2. \((3 * \sqrt{2}) ^ 4\) = \(3^4 * 2 ^ 2\) = 81 * 4 = 324 3. \((401 ^ {1/4})^4\) = 401
Rank from smallest to biggest : 2, 1, 3
Answer (C)




Re: Rank those three in order from smallest to biggest.
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