Maharashtra BoardEnglish MediumSTD 10MathsReal Numbers3 Marks
Question
Prove that following numbers are irrationals:
$\frac{2}{\sqrt{7}}$
✓
Answer
Let us assume that $\frac{2}{\sqrt{7}}$ is rational.
Then, there exist positive co primes a and b such that,
$\frac{2}{\sqrt{7}}=\frac{\text{a}}{\text{b}}$
$\sqrt{7}=\frac{2\text{b}}{\text{a}}$
$\sqrt{7}$ is rational number which is a contradication.
Hence $\frac{2}{\sqrt{7}}$ is irrational
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