Question

show that 4 √5 is an irrational number​

Answer 1

${ \bold {\rm{ \underline{ \underline{ \:To \: \: Prove : 4 \sqrt{5} \: \: is \:an \: \: Irrational \: \: Number }}}}}$

We shall prove this by the method of contradiction .

So let us assume that 4√5 is a rational number such that it can be written as →

$\implies \: 4 \sqrt{5} \: = r \: \\ \\ \implies \: \sqrt{5} = \dfrac{r}{4}$

From this equation , it is clear that √5 is an irrational number . Hence , the R.H.S [ r/4] cannot be rational or else the equation would become false!

Hence , our assumption that 4√5 is rational is wrong.

$\diamond \: \: { \bold { \underline{4 \sqrt{5} \: is \: \: an \: \: irrational \: \: number}}}$