Prove that root 2 + root 5 is irrational
Prove that √2 + √5 is irrational
Let us suppose that √2 + √5 is rational.
Let , where a and b coprime integers and b ≠ 0.
Squaring both side
⇒ √2 is rational, since is rational.
This contradict the fact that √2 is an irrational number.
So, our assumption is wrong.
Hence, √2 + √5 is irrational
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