prove 5+3✓2 is irrational
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Given : 5 + 3√2
To 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/b
5 + 3√2 = a/b
Here a and b are coprime numbers and b ≠ 0
Solving 5 + 3√2 = a/b we get,
=> 3√2 = a/b – 5
=> 3√2 = (a-5b)/b
=> √2 = (a-5b)/3b
This 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 number
Hence proved