Prove that (√2+√5) is Irrational

Answer: A Rational number is an integer that can be expressed in p/q form where q≠0. An irrational number cannot be expressed like that.

Let us assume (√2+√5) is rational.

So, √2+√5 = p/q

Squaring on both sides,

(√2+√5)2 = (p/q) 2

2 + 5 +2 x √2 x √5 = p2/q2

7+2√10 = p2/q2

√10 =1/2[(p2/ q2) – 7]

√10= 3.1622776… it is an irrational number.

A rational number cannot be equal to an irrational number. Therefore, our assumption is false.

Hence, (√2+√5) is irrational.