Question

Show that 5./6
is an irrational number?​

Answer 1

Step-by-step explanation:

Let, 5√6 be a rational number and can be written in the form p/q where p and q are co - prime and q is not equals to zero.

$\frac{5}{ \sqrt{6} } = p /q$

$\frac{5q}{p} = \sqrt{6}$

From above we can see that, 5q/p is a rational number number and in the form of p/q, therefore /√6 is also a rational number.

But this contradicts the fact that √6 is an irrational number. This problem has arrise due to our wrong assumption that 5√6 is a rational number, thus 5√6 is a irrational number.

Hence proved