Question

Among : √17- √12 and √11-√6 which is greater and how?

Answer 1

If any number x is greater than any number y then 1/x<1/y .

Its quite logical if the number is bigger then it will take a lesser quotient to divide a fixed quantity than the number which is less.

3>2 but 1/2>1/3

Similarly just find value of

1/(√17−√12) and 1/(√11−√6)

1/(√17−√12)=(√17+√12)/5 by rationalization

and similarly

1/(√11−√6)=(√11+√6)/5

Now compare the 2 values.Quite logical that

(√17+√12)/5>(√11+√6)/5 (Since they have same denominators )

So 1/(√17−√12)> 1/(√11−√6)

THIS IMPLIES THAT

√11−√6> 17−√12