| The value of \[\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}\]is |
A) \[\frac{3}{4}\]
B) \[1\frac{3}{4}\]
C) \[1\frac{1}{3}\]
D) \[1\frac{7}{9}\]
Correct Answer: C
Solution :
| \[\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}=\frac{\sqrt{16\times 5}-\sqrt{16\times 7}}{\sqrt{9\times 5}-\sqrt{9\times 7}}=\frac{4\sqrt{5}-4\sqrt{7}}{3\sqrt{5}-3\sqrt{7}}\] |
| \[=\frac{4\,(\sqrt{5}-\sqrt{7})}{3\,(\sqrt{5}-\sqrt{7})}=\frac{4}{3}=1\frac{1}{3}\] |
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