Rational and Irrational Numbers — MATHEMATICS STD 9 — Question
ICSE BoardEnglish MediumSTD 9MATHEMATICSRational and Irrational Numbers3 Marks
Question
Prove that $(\sqrt{3}+\sqrt{7})$ is irrational.
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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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