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| 1. |
Prove. That2+5_/3is an irrational |
| Answer» If possible let 2 + 5_√3 be rational number and it is in the form of a÷b , where a and b are co- prime number. 2+5√3= a÷b 5√3 = a÷b - 2. √3 = a÷5b - 2. Here , a and b are integer , and a÷5b -2 is rational number , so √3 is rational , but this contradict the fact that √3 is irrational , this contradiction has arisen because of our incorrect assumption that 2 +5√3 is rational , so 2+ 5√3 is irrational . HENCE PROVED | |