MCQ
The value of $\frac{2}{\sqrt{5}-\sqrt{3}}$ is:
- A$\frac{1}{\sqrt{5}-\sqrt{3}}$
- B$\sqrt{5}-\sqrt{30}$
- ✓$\sqrt{5}+\sqrt{30}$
- D$\frac{2}{\sqrt{5}+\sqrt{3}}$
✓
Answer
Correct option: C.
$\sqrt{5}+\sqrt{30}$
$\frac{2}{\sqrt{5}-\sqrt{3}}$
multiplying nu nominator and denominator by
$\sqrt{5}+\sqrt{3},$ we get
$\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}$
$=\frac{2(\sqrt{5}+\sqrt{3})}{5-3}$
$=\sqrt{5}+\sqrt{3}$
multiplying nu nominator and denominator by
$\sqrt{5}+\sqrt{3},$ we get
$\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}$
$=\frac{2(\sqrt{5}+\sqrt{3})}{5-3}$
$=\sqrt{5}+\sqrt{3}$
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