Rank those three in order from smallest to biggest.

Question

I.  2\sqrt{5}

II.  3\sqrt{2}

III.  \sqrt {401}

(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, II, I

acegmat123 · Accepted Answer

Raise all the options to the power of 4.

I. 2^4* 5^2 = 400

II. 3^4*2^2 = 324

III. 401

II < I < III

C

Edited calculation error

Sent from my iPhone using  GMAT Club Forum mobile app

Vinayak Shenoy · Answer

IMO C
2 sqrt5= 2*2.236= 4.472
3 sqrt2= 3* 1.414= 4.242
(401)^(1/4) = 4.475 (1, 16, 81, 256, 625) === (401)^(1/4) will fall between 256 and 625

Vinayak Shenoy · Answer

Raise all the options to the power of 4. I. 2* 5^2 = 50 II. 3*2^2 = 12 III. 401 II < I < III C 1 is 16*25= 400 2 is 81*4=324 3 is 401 Liked your style of solution though

i went the conventional way. Took me a bit more time than this solution

GSBae · Answer

Put all numbers into their most basic square root forms.

I.  2\sqrt{5}   =  \sqrt{4*5} = \sqrt{20} 
 
II.  3\sqrt{2}    =  \sqrt{9*2}  =  \sqrt{18}

III.  \sqrt {401}  . This one is a bit more difficult. To take the 4th root is to take the square root twice. The square root of 401 is slightly more than 20, so the 4th root of 401 will be slightly more than  \sqrt{20} .

Thus, our ordering from smallest to largest is II,I,III.

Answer: C

AK125 · Answer

For the last step I would suggest to bring  \sqrt{20}  to  2\sqrt{5}  , which is a little bit smaller than I

Abhishek009 · Answer

I.  (2\sqrt{5})^2  = 20 &  20^2  =  400 
II. (3\sqrt{2})2  = 18 &  18^2  =  324 
III. (\sqrt {401})^4  =  401

So, Ascending order of arrangement will be II, I, III , answer will be (C)

GMATinsight · Answer

Best way to answer such questions is APPROXIMATION

I.  2\sqrt{5}  = 2*2.25 = 4.5

II.  3\sqrt{2}  = 3*1.41 = 4.2

III.  \sqrt {401}  =  \sqrt{20}  = 4.49

Answer: Option C

rahul16singh28 · Answer

Best way to answer this is  a^4 = 400, b^4 = 162, c^4 = 401 .. Now if we have doubt in this try a^4 - b^4 = (a-b)(a+b)(a^2+b^2) .. Similarly, c^4 - a^4, c^4 - b^4

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Rank those three in order from smallest to biggest.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Rank those three in order from smallest to biggest.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards