Given that √2 is irrational, prove that (5 + 3 √2) is an irrat

1.	Given that √2 is irrational, prove that (5 + 3 √2) is an irrational number.
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 ≠ 0 (p -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.

Given that √2 is irrational, prove that (5 + 3 √2) is an irrational number.

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 ≠ 0

(p -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.