InterviewSolution
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InterviewSolution
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Show that (2 + sqrt(3)) is an irrational number. |
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Answer» Solution :Let, if possible `(2 + sqrt(3))` is RATIONAL then, `2 + sqrt(3) = (a)/(b)` (say) where, a and b are integers and `b ne 0`. `rArr` `sqrt(3) = (a)/(b) - (2) ""rArr"" sqrt(3) = (a - 2b)/(b)""`…(1) `because` a and b are integers `therefore` a - 2b is also an integer. `rArr` `(a - 2b)/(b)` is rational. Now, L.H.S. of equation (1) is the square root of a prime number. So, it is irrational and R.H.S. is rational. Which is a contradiction because a rational number and an irrational number can never be equal. So, our supposition i.e., `2 + sqrt(3)` is rational, is WRONG. Hence, `(2 + sqrt(3))` is an irrational number. `""` Hence Proved. |
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