Question

prove that 2✓2+2✓3 can't be rational number

Answer 1

Hey MATE!

Let us assume that the above is a rational number.

Therefore,

$2 \sqrt{2} + 2 \sqrt{3} = \frac{p}{q} \\ squaring \: both \: the \: sides \: we \: get \\ \\ ( {2 \sqrt{2} + 3 \sqrt{2} } )^{2} = ({ \frac{p}{q} })^{2} \\ = > 8 + 18 = 6 \sqrt{4} = ({ \frac{p}{q} })^{2} \\ 8 + 18 + 12 = \frac{ {p}^{2} }{ {q}^{2} } \\ \frac{38}{1} = \frac{ {p}^{2} }{ {q}^{2} } \\ \frac{p}{q} = \sqrt{38}$
Since rational ≠ Irrational.

Therefore the above number is Irrational.

Hope it helps

Hakuna Matata :))