Question
Prove that $(\sqrt{3}+\sqrt{7})$ is irrational.

Answer


[Hint. If possible, let $(\sqrt{3}+\sqrt{7})$ be rational.
Then, $(\sqrt{3}+\sqrt{7})^2$ is rational.
But, $(\sqrt{3}+\sqrt{7})^2=(3+7+2 \sqrt{21})=(10+2 \sqrt{21})$, which is clearly irrational.
So, our supposition is wrong.]

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