Question

prove that root 2 and root 3 is irrational

Answer 1

it gives in some decimal point

Answer 2

let√2 be rational
√2=a/b where a and b are co primes
(√2)^2=(a/b)^2
2=a^2/b^2
2b^2=a^2
2 | a^2
2 | a

a=2c for some integer c
a^2=4c^2
2b^2=4c^2
b^2=2c^2
2 | b^2
2 | b

From this we get that 2 is the common factor of a and b. But this contradiction is wrong . Therefore √2 is irrational.
√3 will be in the similar way.
Hope this will help you.