Saved Bookmarks
| 1. |
Prove root5 is an irrational number |
| Answer» let root 5 be rationalthen it must in the form of p/q [q is not equal to 0][p and q are co-prime]root 5=p/q=> root 5 * q = psquaring on both sides=> 5*q*q = p*p ------> 1p*p is divisible by 5p is divisible by 5p = 5c [c is a positive integer] [squaring on both sides ]p*p = 25c*c --------- > 2sub p*p in 15*q*q = 25*c*cq*q = 5*c*c=> q is divisble by 5thus q and p have a common factor 5there is a contradictionas our assumsion p &q are co prime but it has a common factorso\xa0√5 is an irrational | |