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| 1. |
Prove that √7 is irrational |
| Answer» Let us assume that √7 be rationalThen it must in the form of p/q (q#0) { p and q are co-prime } √7=p/q=> √7 × q=pQuiring on both sides=> 7q2 = p2 ------->(1)p2 is divisible by 7 p is divisible by 7p=7c (c is a positive integer) (squaring on both side)p2=49c2--------> (2) substitute p2 in equipment (1) we get7q2=49c2=>q is divisible by 7Thus q and p have a common factor 7there is a contradictionas our assumption p&q are co-prime but it has a common factorSo that √7 is an irrational. | |