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Simplify \(\frac{20}{5\sqrt{28} - 2 \sqrt{63}}\)


Question

Simplify \(\frac{20}{5\sqrt{28} - 2 \sqrt{63}}\)

Options

A) \(\frac{5\sqrt{7}}{7}\)

B) \(\frac{5\sqrt{5}}{7}\)

C) \(\frac{7\sqrt{5}}{7}\)

D) \(\frac{7\sqrt{7}}{5}\)

The correct answer is A.

Explanation:

\(\frac{20}{5 \sqrt{4 \times 7} - 2\sqrt{9 \times 7}}\)

\(\frac{20}{10 \sqrt{7} - 6\sqrt{7}}\)

= \(\frac{20 \sqrt{7}}{4 \sqrt{7}}\)

= \(\frac{5\sqrt{7}}{7}\)


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Dicussion (1)

  • \(\frac{20}{5 \sqrt{4 \times 7} - 2\sqrt{9 \times 7}}\)

    \(\frac{20}{10 \sqrt{7} - 6\sqrt{7}}\)

    = \(\frac{20 \sqrt{7}}{4 \sqrt{7}}\)

    = \(\frac{5\sqrt{7}}{7}\)

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