Question

Is 2 + root 3 a rational or a irrational number? why?

Answer 1

It is irrational becoz it cannot be written in the formation of p/q where quality not equal to 0 .

Answer 2

it is an irrational number.
let √2 + √3 is a rational number
√2 + √3 = p/q
p/q - √3 = √2
squaring both sides
p²/q² + 3 - 2 p/q √3 = 2
p²/q² + 3 - 2 = 2 p/q √3
p²/q² + 1 = 2 p/q √3
(p² + q²)/q/2p = √3
(p² + q²)/2pq = √3
√3 is irrational no.
(p² + q²)/2pq is rational no.
hence, 2 + √3 is irrational