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# Rank those three in order from smallest to biggest.

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4487
Rank those three in order from smallest to biggest.  [#permalink]

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27 Sep 2016, 17:20
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:40) correct 41% (01:38) wrong based on 120 sessions

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Attachment:

three roots.png [ 34.21 KiB | Viewed 1781 times ]

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, I

This 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 GMAT

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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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, I

This 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 GMAT

Mike

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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2
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

Intern
Joined: 10 Jun 2019
Posts: 9
Re: Rank those three in order from smallest to biggest.  [#permalink]

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21 Jun 2019, 00:38
Approached the question by trying to find the 4th power of all the choices so as to eliminate the 4th root of 401 in Choice III. In doing so, we get
Choice I - 400
Choice II - 324
Choice III - 401

So arranging from smallest to largest, we get II < I < III. Hence, Option C is the right answer.
Re: Rank those three in order from smallest to biggest.   [#permalink] 21 Jun 2019, 00:38
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