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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.
