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| 1. |
If √2 is an rational number |
| Answer» Assume √2 as rational√2 = a/b ( where a and b are co- prime) co-prime - no\'s having 1 as common factorSquaring on both sides2 = a^2/b^22b^2 = a^2----12 divides a^2 & a alsoa = 2 cSquaring on both sides a^2 = 4c^2----2From 1 & 2 2b^2 = 4c^2b^2 = 2c^2b^2/2 = c^ 2This shows 2 divides b^2 & b also Hence 2 is a common factor for a and b,this contradicts the fact that a and b are co- prime.so,our assumption is wrong.Therefore, √2 is Irrational. | |