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| 1. |
Prove √5 irrational |
| Answer» Let √5=a/b. (Where a nd b are co prime integers)Squaring both sides5=a^2/b^2a^2=5b^2. ------(1)5 is a factor of a^2So 5 is afactor of a alsoLet a=5cSquaring both sidesa^2=25c^25b^2=25c^2. -------(from1)b^2=5c^25 is a factor of b^2So 5 is a factor of b also since 5 is a factor of both a and b This is contradiction Our supposition is wrong √5 is irrational | |