Question

Prove that √2+√5 is irrational

Answer 1

Let √2+√5 be a rational number.
A rational number can be written in the form of p/q.
√2+√5=p/q

Squaring on both sides,

(√2+√5)²=(p/q)²
[√2²+√5²+2(√2)(√5)]=p²/q²
(2+5+2√10)=p²/q²
2√10+7=p²/q²
2√10=p²/q²-7
2√10=(p²-7q²)/q²
√10=(p²-7q²)/2q²

p,q are integers then (p²-7q²)/2q is a rational number.
Then,√10 is also a rational number.
But this contradicts the fact that √10 is an irrational number.
So,our supposition is false.
Therefore, √2+√5 is an irrational number.
Hence proved.

Answer 2

Step-by-step explanation:

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