Aptitude - Square Root and Cube Root - Discussion

Discussion :: Square Root and Cube Root - General Questions (Q.No.2)

2. 

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

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

Answer: Option A

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: (Oct 30, 2011)  
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: (Jan 8, 2012)  
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: (Sep 2, 2012)  
@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: (Oct 9, 2012)  
Is there any short tricks to find square root and cube root ?

Proek said: (Oct 16, 2012)  
-12 is the valid answer too!

Jiyan Prathap said: (Dec 23, 2012)  
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: (Dec 30, 2012)  
@Jiyan prathap. Can we find square root of all others too by using this method?

Pradeep said: (Apr 8, 2013)  
128*162 = 20736.

Now find the square root by long division method.

Square root = 144.

Thus x = 12.

Ravi said: (Oct 23, 2013)  
@Jiyan prathap.

By using your method find the square root of 196.

Govind said: (Feb 18, 2014)  
The above said method is easy to find. Because we can split the no by using the square values we know.

Lavanya said: (Jul 17, 2014)  
Shortcut method is applicable to only number 144 its not applicable to all 3 digit number. Try to give shortcut method to all numbers.

Harshi said: (Aug 24, 2014)  
Your method is not correct the sqrt of 169 is 13 by your method it is also 12.

Sameer said: (Oct 17, 2014)  
X = square root 128*162

= square root 64*2*81*2

= square root 64*81*4

= 8*9*2 = 144

Why answer is showing 12?

Kavya K said: (Oct 21, 2014)  
@Sameer, that's not X = square root 128*162.

It should be X^2 = square root 128*162.

= square root 64*2*81*2.

= square root 64*81*4.

= 8*9*2.

X^2 = 144.

=> X = 144/2.

= 12.

Chandu said: (Oct 26, 2014)  
@Sameer.

x square = 144.
Then x = square root of 144.
x = 12.

Azam said: (Jan 21, 2015)  
Short method is that first take LCM of number given then make pairs.

Hammad said: (Mar 2, 2015)  
We only find the value of x which is equal to 144. But 12 is the square root of 144. If we looking on the question he only demand the value of x which we find initially.

Mani Ratan said: (Jun 9, 2015)  
Can we do 162=81*2 please solve it by other process?

Annoy Singh said: (Sep 20, 2015)  
Because x = 144.

x = 12*12=144.

Parag said: (Oct 27, 2015)  
What is the meaning of ^?

Feroz said: (Nov 11, 2015)  
@Jiyan prathap.

This is not working to roots I thinks so but it useful for me.

Pbk said: (Apr 28, 2016)  
@Parag.

Meaning of ^(Circumflex/Caret).

Circumflex : It is a symbol used to represent a number to the power of the other number. The symbol of circumflex is ^. This symbol is also referred as Hat or Caret.

Example:-
2^3 (ie:- 2 to the power of 3).
2^3 = 2*2*2.

Mahesh said: (Dec 26, 2016)  
Thanks @Sameer.

Apeksha said: (Feb 27, 2017)  
x^2 = root of 128 * 162.
= root of 20736.
x^2 = 144,
x = root of 144,
x = 12.

Pranav said: (Jun 5, 2017)  
How to solve it? I am getting confuse, Please tell me.

Siva Sai said: (Jul 4, 2017)  
Well Explained. Thank You.

Chsony said: (Jul 15, 2017)  
Nice explanations, Thanks.

Bishnu said: (Jul 23, 2018)  
Nice. Thanks for the explanation.

Vivek said: (Nov 11, 2019)  
If I use 81 *2 in place of 162 then? In 81 *2, 81 is also a perfect square.

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