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# Aptitude - Square Root and Cube Root - Discussion

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"It takes a very long time to become young."
- Pablo Picasso
2.

 What should come in place of both x in the equation x = 162 . 128 x

 [A]. 12 [B]. 14 [C]. 144 [D]. 196

Explanation:

 Let x = 162 128 x

Then x2 = 128 x 162

= 64 x 2 x 18 x 9

= 82 x 62 x 32

= 8 x 6 x 3

= 144.

x = 144 = 12.

 S.Ramkumar said: (Sun, Oct 30, 2011 11:49:12 PM) You split 162=18*9 how we can understand this because there are so many possibles are there to split 162 and how we can find this exact split.

 Sreedevi said: (Sun, Jan 8, 2012 07:38:04 AM) You can see that 162 is divisible by 9.i.e.(1+6+2)=9 which is a multiple of 9.so it makes calculation easier if one factor is a perfect square. You can split 162 as 81*2 also where 81 is a perfect square.

 Kumari said: (Sun, Sep 2, 2012 06:57:06 PM) @sreedevi, Thanks for tip. But,I think it is bit difficult to get this correctly. Mostly we need to think in terms of squares and then look for which one will give 162

 Sumi said: (Tue, Oct 9, 2012 10:41:21 PM) Is there any short tricks to find square root and cube root ?

 Proek said: (Tue, Oct 16, 2012 09:10:41 PM) -12 is the valid answer too!

 Jiyan Prathap said: (Sun, Dec 23, 2012 07:49:26 PM) There is a short cut to find square root For Eg: 144 which is the square of 12. First leave the last two digits of 144. The remaining is 1, 1 comes in 1 table alone. Hence the first number of the answer is 1. To find the second digit always add 1 to the first digit of the answer i.e 1+1=2 which is the second digit. Combine together the answer is 12.

 Kalyani said: (Sun, Dec 30, 2012 07:33:33 PM) @Jiyan prathap. Can we find square root of all others too by using this method?

 Pradeep said: (Mon, Apr 8, 2013 08:25:45 PM) 128*162 = 20736. Now find the square root by long division method. Square root = 144. Thus x = 12.