Question

Show that 5+√2 is irrational number

Answer 1

let 5+ root 2 is rational number.
5+root2=a/b
root 2=5+a/b=(5b+a)/b
here,the number is again in a/b form.so it is a rational no.
root 2 is ratioal no.
it contradicts te fact that root 2 is irrational 
our consumption is wrong
therefore,5+root 2 ia a irrational

Answer 2

Here √2 is irrational number because it is non terminating and non recurring number. So 5 + √2 is irrational because we are trying to add 5 with an irrational number. If we add any number with irrational number it will be always irrational.