Question

prove that √2 + √5 is irrational

Answer 1

1st method:-

√2 = 1.414....

√5 = 2.236....

so,

√2 + √5

= 1.414...+ 2.236....

= 3.65....

since non terminating numbers are irrational so, this is irrational.

2nd method :-

Both √2 and √5 are non terminating as given above.

so, √2 and √5 are irrational numbers.

And sum of two irrational numbers is irrational.