Question

prove that 8-√6 is irrational​

Answer 1

Explanation:

Let us assume that 6 is rational number. 

Then it can be represented as fraction of two integers.

 Let the lowest terms representation be: 6=ba where b is not equal to 0

Note that this representation is in lowest terms and hence, a and b have no common factors

2=6b^2

From above a^2 is even. If a^2 is even, then a should also be even.

⟹a=2c

4c^2=6b^2

2c2=3b2

From above 3b^2 is even. If 3b^2 is even, then b^2 should also be even and again b is even.

But a and b were in lowest form and both cannot be even. Hence, assumption was wrong and hence, 6 is an irrational number.