Question

Prove that 2+✓6 is an irrational number.
Plz tell answer step by step​

Answer 1

Answer:

2+√6

= √2 x √2 + √2 x √3

= √2(√2+√3)

Answer 2

Let 2 + √6 = a/b

where a, b are integers and b ≠ 0

√6 = a/b - 2

√6 = ( a - 2b ) / b

Since a, b are integers LHS = ( a - 2b )/b is also a rational and hence √6 is rational. But this contradicts the fact that √6 is irrational. Hence our assumption is wrong and 2 + √6 is irrational.