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