Question

Prove that √2+√5 is irrational

Answer 1

HI FRIEND:

Assume that the sum is rationial
2–√+5–√=ab2+5=ab

where aa and bb are integers with b≠0b≠0. Now rewrite this as
5–√=ab−2–√.5=ab−2.

Squaring both sides :
5=a2b2−22–√ab+2.5=a2b2−22ab+2.

Now, solve for 2–√2 and obtain

2–√=−3b2a+a2b.2=−3b2a+a2b.

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

2–√+5–√2+5

so,,,
is an irrational number.

HENSE THE PROOF.......

Hope this helps u...