Saved Bookmarks
| 1. |
Show that root 7 is irrational number |
| Answer» let us assume that √7 be rational.then it must in the form of p / q [q ≠ 0] [p and q are co-prime]√7 = p / q=> √7 x q = psquaring on both sides=> 7q2= p2 ------ (1)p2 is divisible by 7p is divisible by 7p = 7c [c is a positive integer] [squaring on both sides ]p2 = 49 c2 --------- (2)Subsitute p2 in equ (1) we get7q2 = 49 c2q2 = 7c2=> q is divisible by 7thus q and p have a common factor 7.there is a contradictionas our assumsion p & q are co prime but it has a common factor.So that √7 is an irrational. | |