Question on: SS3 Mathematics - Surd
Simplify \(\frac{\sqrt{28}}{2\sqrt{35}}\)
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A
\(5\sqrt{5}\)
B
\(\frac{7\sqrt{5}}{10}\)
C
\(\frac{3\sqrt{5}}{5}\)
D
\(\frac{\sqrt{5}}{5}\)
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Correct Option: D
\[\frac{\sqrt{28}}{2\sqrt{35}} = \ \frac{\sqrt{4 \times 7}}{2\sqrt{35}} = \frac{2\sqrt{7}}{2\sqrt{35}} = \frac{2\sqrt{7}}{2\sqrt{35}}.\frac{\sqrt{35}}{\sqrt{35}} = \ \frac{2\sqrt{7 \times 35}}{2 \times 35} = \frac{2\sqrt{7 \times 7 \times 5}}{70} = \frac{2\sqrt{49 \times 5}}{70}\]
\(= \frac{2 \times 7\sqrt{5}}{70} = \frac{14\sqrt{5}}{70} = \frac{\sqrt{5}}{5}\)
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