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Prove 5+3✓2 is irrational |
| Answer» 5 + 3√2To prove : 5 + 3√2 is an irrational number.Proof:Letus assume that 5 + 3√2 is a rational number.Soit can be WRITTEN in the form a/b5 + 3√2 = a/bHere a and b are coprime NUMBERS and b ≠ 0Solving 5 + 3√2 = a/b we get,=> 3√2 = a/b – 5=> 3√2 = (a-5b)/b=> √2 = (a-5b)/3bThis shows (a-5b)/3B is a rational number. But we know that But √2 is an irrational number.so it CONTRADICTS our assumption.Our assumption of 5 + 3√2 is a rational number is incorrect.5 + 3√2 is an irrational numberHence proved | |