Aptitude - Square Root and Cube Root - Discussion

The square roots are nothing but raised to 1/2. 128' and 162'.

So we can simply take that up and down respectively to make them squares of x.

Now, if we consider 12 and 14 from the options, their squares are 144 and 196 respectively, if we put both in place of x' and consider the ratios, we get that 144/128 and 162/144 and dividing these by 16 and 18 respectively we get the ratios to be equal i.e. 9:8.

But the ratios are not the same in the case of 196.

So, the answer is 12.

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.

@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.

X/√128=√162/X.
By cross multiplication,

X x X=√162 x √128,
X^2 = √162 x 128,
X^2 = √20736,
X^2 = √2^8 x 3^4,
X^2 = 2^4 x 3^2,
X^2 = 16 x 9.
X^2 = 144.
X = √144.
X= 12.

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.

@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.

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.

@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

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.

Shortcut method is applicable to only number 144 its not applicable to all 3 digit number. Try to give shortcut method to all numbers.