Question

show that
$\sqrt{2 } + \sqrt{3}$
is irrational ??????
please it's urgent

Answer 1

hey !!!

let √2 + √3 is rational no.

so, also let (√2 +√3 ) is a

(√2+√3) = a

(√3 )²=(a -√2 )² [ squaring on both side ]

=> 3 = a²+ 2 - 2a√2

=> 2a√2 = a² -3+2

=> 2a√2 = a²-1

=> √2 = a² -1 / 2a

but this impossible ,as the right hand side is rational , whether √w is irrational ..

this is contradiction

since , our hypothesis is wrong that [√2 + √3 ]

is rational no. it is an irrational non

so, [√2+ √3 ] is rational no.

hope it helps !!!

#Rajukumar111