Question

Prove irrational : 10_/2+7_/3

Answer 1

Let 10√2 + 7√3 = (a/b) is a rational no.
On squaring both sides , we get 200 + 147 + 140√6 = (a2/b2)
So,347 + 140√6 = (a2/b2) a rational no.
So, 140√6 = (a2/b2) – 347
Since, 140√6 is an irrational no.
and (a2/b2) – 347 is a rational no.
So, my contradiction is wrong.
So, (10√2 + 7√3) is an irrational no.