1.

Among `sqrt(7)-sqrt(3)andsqrt(11)-sqrt(7)` which is greater?

Answer» By rationalizing ,
`sqrt(7)-sqrt(3)=((sqrt(7)-sqrt(3))(sqrt(7)+sqrt(3)))/(sqrt(7)+sqrt(3))=(4)/(sqrt(7)+sqrt(3))`
`sqrt(11)-sqrt(7)=((sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7)))/(sqrt(11)+sqrt(7))=(4)/(sqrt(11)+sqrt(7))`
The numberator of each of the irrational number is 4.
But `sqrt(11)+sqrt(7) gt sqrt(7)+sqrt(3)`
`therefore (4)/(sqrt(7)+sqrt(3)) gt (4)/(sqrt(11)+sqrt(7))`
`sqrt(7)-sqrt(3) gt sqrt(11)-sqrt(7)`


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