1)The first qn is from Gprep exam and its a wrongly printed one on the screen.
Its already discussed in other topics here.
The question should read as 2^ (x+y)^2 / 2^(x-y)^2
which will lead to answer 16 when xy = 1
2) We need to find the square root of the surds.
There's a method we learn in our high school here.
say you want to find sq.rt( 9 + sq.rt(80) ) where sq.rt is the square root
Follow the below steps to arrive at answer
a. we should always try to extract 2 out of the inner sq. rt . i.e sq.rt(80) = sq.rt(4*20) = 2 * sq.rt(20)
b. Now you should check if the number left in the inside sq.rt after extraction of 2...i.e 20 here has two factors whose sum is equal to the remaining number in the outer square root. i.e 9 here. Usually this is done by trivial observation
what i mean is 20 = 4* 5 and 4+ 5 = 9 (the isolated number in sq.rt)
c. after that observation you can simply write the result as sq.rt(5) + sq.rt(4) = sq.rt(5) + 2
sq.rt( 9 + sq.rt(80) ) = sq.rt(5) + 2
similarly sq.rt( 9 - sq.rt(80) ) = sq.rt(5) - 2 (simply inserting - sign between a large and small number)
Hence given problem reduces to (2 sq.rt(5) ) ^2 = 4*5 = 20
20 is the answer.
Believe me, By a little practice you can solve such qns by simple observations !! No pen or pencil on paper..
Neo
MBA : My passion and My pursuit
