Question

is
$\sqrt{2}$
prove it is a irrational no .. with many process and also
$\sqrt{3}$
is an irrational no.

Answer 1

hey there here is your answer

let us assume that root 2 is rational
so, it can be written in the form of p by q where p and q are co primes
√2 = p/q
p = √2q
squaring both sides
p² = 2q²-------(i)
so, 2 divides p²
2 divides p
so, we can write p as a factor of 2
now, let
p = 2r
squaring both sides
p² =4r²------(ii)
comparing equation i & ii we get
2q² = 4r²
=> q² = 2r²
so 2 divides q² and
2 divides q
so we can write q as a factor of 2
here p & q what are the factors of 2
this contradict the fact that p and q are co primes
so, our assumption is wrong
hence root 2 is irrational

in the same way you can prove root 3 as irrational

hope it helps plz mark as brainlest