Saved Bookmarks
| 1. |
nu TUOTII UTOIT On saanu punu AAOUT UpidxTZ3. Examine, whether the following numbers are rational or irrational:(i) 7(ii) 4(iii) 2 + 3 |
|
Answer» √4=2 hence it is rational 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=> 7q^2= p^2------> (1)p^2is divisible by 7p is divisible by 7p = 7c [c is a positive integer] [squaring on both sides ]p^2= 49 c^2--------- > (2)subsitute p^2in equ (1) we get7q^2= 49 c^2q^2= 7c^2=> q is divisble 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. (i) &(iii) are irrational (ii) is rational 7 is not a perfect square root 7 is a irrational number. 4 is square of 2.so root 4 is a rational number. 2+root3 is a irrational number. sum of rational and irrational is a irrational number. |
|