Question

Prove that in √3+√5 is an irrational Number
with explanation ​

Answer 1

Answer:

$\huge\fcolorbox{blue}{pink}{☃αղsաҽɾ☃}$

$\bold{To \: Prove : \sqrt{3} + \sqrt{5} \: is \: irrational } \\ \\ \bold{let \: us \: assume \: it \: to \: be \: a \: rational \: number} \\ \\ \bold{ ⇒ \: \sqrt{3} + \sqrt{5} = \frac{p}{q} } \\ \\ \bold{⇒ \: \sqrt{3} = \frac{p}{q} - \sqrt{5} } \\ \\ \bold{♡ \: squaring \: both \: sides \: ♡}$

$\bold{⇒ \: 3 = \frac{p ^{2} }{q ^{2} } - 2 \times \sqrt{5} \: \: \binom{p}{q} + 5}$