**Quote:**

hi

"Multiplying and dividing the expression by √10 does not change the value of the expression" that's okay ..but can you please tell me why the following method - squaring the whole expression - is not working here

(√x + √y) / √(x + y)

= { (√x + √y) / √(x + y) } ^ 2

thanks in advance

Hi

gmatcracker2017it will work but the problem is the options are not in their simplest form. Hence you will have to undertake lot of calculation to arrive at the answer choice.

Straight forward Algebric method would be -

\((\sqrt{x}+\sqrt{y})/\sqrt{x+y}\), multiply the numerator and denominator by \(\sqrt{x+y}\) to get

\((\sqrt{x}+\sqrt{y})(\sqrt{x+y})/x+y\) \(=(\sqrt{x(x+y)}+\sqrt{y(x+y)})/x+y\). Now substitute the values of \(x\) & \(y\) to get

\((\sqrt{40}+\sqrt{60})/10\) \(=(\sqrt{10}+\sqrt{15})/5\)

Option

D