Question

prove that root 2 + 3 root 5 is irational​

Answer 1

Let √2+3√5 be rational no.

Then, √2+3√5= $\frac{a}{b}$

where, a and b are positive integers, and b≠0

So,

√2+3√5= $\frac{a}{b}$

√2+√5= $\frac{a}{3b}$

$\frac{a}{3b}$ = $\frac{integer}{integer}$ ...(1)

and,

√2+√5= irrational + irrational = irrational...(2)

so, from (1) and (2)

we get,

irrational = rational

{which is not possible}

$\therefore$ OUR SUPPOSITION IS WRONG...

√2+3√5 ...IS NOT RATIONAL...IT IS IRRATIONAL!

$<marquee><strong><em>HENCE</em></strong><strong><em> </em></strong><strong><em>PROVED</em></strong><strong><em>!</em></strong><strong><em>❤︎</em></strong><strong><em> </em></strong></marquee>$