Question

prove that 8-√6 is irrational​

Answer 1

Answer:

Let 8-$\sqrt{6$ be a rational number.

Therefore 8-$\sqrt{6}$ = p/q where q not equal to zero , pand q are integers and they do not have any other common prime factors other than zero.

therefore, 8-\sqrt{6} = p/q

\sqrt{6}=-p+8/q

therefore the rhs is a rational number

But we know that sqrt of 6 is an irrational number as square roots of prime numbers are irrational

therefore lhs not equal to rhs

given number is irrational