Question

prove that √2+ √5 is irrational number
please tell me it's solution step by step

Answer 1

Use proof by contradiction. Assume that the sum is rationial,
that is

root 2+ root 5 = a/b

where a and b are integers with b≠0. Now rewrite this as

root 5 = a/b - root 2

Squaring both sides of this equation we obtain

5=a square b square −2 root 2 a/b + 2

Now, carefully solve for root 2 and obtain

root 2 = -3b/2a + a/2b

This implies that root 2  is a rational number which is a contradiction. Thus

root 2 + root 5

is an irrational number.