Question

given that √2 is irrational so proove that 5+3√2 is also irrational

Answer 1

lets assume√2 is an rational no.
let us divide √2 by a and b to get at least one common factor other than 1
√2=a\b
sq.both sides
(√2)*2=a*2\b*2
2= a*2\b*2
2b*2=a*2
hence,,a*2 is divisible by 2
so, a is also divisible by 2


now let's assume a=2c
2b*2=(2c)*2
2b*2=4c*2
b*2= 2c*2
b*2 is divisible by 2
b is also divisible by 2

therefore √2 has at least 2 common factor
it contradicts the fact that it has at least two common factor other than 1.
our supposition went wrong that it is an rational number

hence proved.......√2 is an irrational number