Simplify without using tables \(\frac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}\)
A. \(\frac{3\sqrt{14}}{4}\)
B. \(\frac{3\sqrt{2}}{4}\)
C. \(\frac{3\sqrt{14}}{28}\)
D. \(\frac{3\sqrt{2}}{28}\)
Correct Answer: D
Explanation
\(\frac{2\sqrt{14} \times 3\sqrt{21}}{7 \sqrt{24} \times 2\sqrt{98}}\) = \(\frac{6\sqrt{14} \times 3 \times \sqrt{7} \times \sqrt{3}}{7 \times 2 \sqrt{6} \times \sqrt{7} \times \sqrt{14}}\)
= \(\frac{3\sqrt{3}}{14\sqrt{6}}\)
= \(\frac{3\sqrt{3}}{14\sqrt{2} \times \sqrt{3}}\)
= \(\frac{\sqrt{3}}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)
= \(\frac{3\sqrt{2}}{28}\)
