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Simplify \(\frac{4\sqrt{18}}{\sqrt{8}}\)


Question

Simplify \(\frac{4\sqrt{18}}{\sqrt{8}}\)

Options

A) 2

B) 3

C) 6

D) 12

The correct answer is C.

Explanation:

\(\frac{4\sqrt{18}}{\sqrt{8}}\\= \frac{4\sqrt{9\times 2}}{\sqrt{4 \times 2}} = \frac{12\sqrt{2}}{2\sqrt{2}}=\frac{6\sqrt{2}}{\sqrt{2}}\\Rationalising \frac{6\sqrt{2}}{\sqrt{2}}\\=\frac{6\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 6\)

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Dicussion (1)

  • \(\frac{4\sqrt{18}}{\sqrt{8}}\\= \frac{4\sqrt{9\times 2}}{\sqrt{4 \times 2}} = \frac{12\sqrt{2}}{2\sqrt{2}}=\frac{6\sqrt{2}}{\sqrt{2}}\\Rationalising \frac{6\sqrt{2}}{\sqrt{2}}\\=\frac{6\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 6\)

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