Question

prove 5 root 6 is irrational no

Answer 1

Assume that 5√6 is a rational number.

Let x = 5√6, where x is a rational number which values 5√6.

$\displaystyle x=5\sqrt{6} \\ \\ \\ \frac{x}{5}=\sqrt{6}$

Here it seems that √6 can be written as a fraction, like in p/q form. But √6 is actually an irrational number so that it can't be written as a fraction.

Thus a contradiction occurs, thereby being our earlier assumption wrong.

Hence proved that 5√6 is irrational.