Aptitude - Square Root and Cube Root - Discussion

Thanks all for explaining the answer.

Well explained, Thanks all.

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.

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.

X^2 = √(162*128).
= √20736.
X^2 = 144.
And X = 12.

X^2 = √128x√162
X^2 = 8√2x9√2
X^2 = 72x2
X^2 = 144
X = √144.
X = 12.

If I use 81 *2 in place of 162 then? In 81 *2, 81 is also a perfect square.

Nice. Thanks for the explanation.

Nice explanations, Thanks.

Well Explained. Thank You.