Question

Prove that (5+3√2) is irrational.​

Answer 1

Answer:

Let 5 + 3√2 be a rational number

5 + 3√2 = P / q

Where q ≠ 0 and p and q are co- prime number

3√2 = P / q - 5√2 = p -5q / 3q

p and q are integers and g ≠ 0p -5q / 3q is rational number √2 is a rational number but √2 is irrational number.This contradiction has arisen because our assumption is wrong. So we conclude that 5+3√2 is an irrational number.

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