Which of the following values is greater than [m]\sqrt{2}[/

Question

Which of the following values is greater than  \sqrt{2} ?

i.  \sqrt {3} 
ii.  \sqrt {4} 
iii.  \sqrt {5}

A. i only
B. ii only
C. iii only
D. i and iii
E. i, ii and iii

Posted from my mobile device

firas92 · Accepted Answer

\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{3}{6}}=8^{\frac{1}{6}}

And,  \sqrt{2}=2^{\frac{1}{2}}=2^{\frac{2}{4}}=4^{\frac{1}{4}}

And,  \sqrt{2}=2^{\frac{1}{2}}=2^{\frac{5}{10}}=32^{\frac{1}{10}}

i.  \sqrt {3}=3^{\frac{1}{3}}=3^{\frac{2}{6}}=9^{\frac{1}{6}}

So i is greater than  \sqrt{2}

ii.  \sqrt {4}=4^{\frac{1}{4}}

So ii is not greater than  \sqrt{2}

iii.  \sqrt {5}=5^{\frac{1}{5}}=5^{\frac{2}{10}}=25^{\frac{1}{10}}

So iii is not greater than  \sqrt{2}

Answer is  (A)

Posted from my mobile device

amoghhlgr · Answer

Isn't  \sqrt {3}^{3}  = 3?

By doing that, I got  \sqrt {5}  as the only possible value greater than  \sqrt{2} ..

Any advice?

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem Series ↧↧↧

https://www.youtube.com/watch?v=EWpKOxOK_vc

B.  \sqrt {4}  =  \sqrt {4}  =  (2)^(\frac{2}{4})  =  \sqrt{2}

Now, we need to compare  \sqrt{2} ,  \sqrt {4}  and  \sqrt {5}

let's make the power integer for all of them for easier comparison.
We can do that by raising all the numbers by power of LCM of the denominators of the powers
=> LCM(2,3,5) = 2*3*5 = 30

=> We need to compare  (2)^(\frac{30}{2}) ,  (3)^(\frac{30}{3})  and  (5)^(\frac{30}{5}) 
 => We need to compare  2^{15} ,  3^{10}  and  5^6

1. Lets compare    2^{15}  and  3^{10}  
 2^{(3*5)}  and  3^{(2*5)} 
=>  8^5  and  9^5 
And we know that  9^5  >  8^5 
 =>  \sqrt {3}  >  \sqrt {2}

2. Lets compare    2^{15}  and  5^6  
 2^{(5*3}  and  5^{(2*3)} 
=>  32^3  and  25^3 
And we know that  32^3  >  25^3 
 =>  2^15  >  5^6

=>   \sqrt {3}  >  \sqrt {2}  >  \sqrt {5}

So,  Answer will be A 
Hope it helps!

Watch the following video to MASTER Roots

https://www.youtube.com/watch?v=5oAec-Y6kOQ

Which of the following values is greater than [m]\sqrt{2}[/

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

Which of the following values is greater than [m]\sqrt{2}[/

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