Correct Answer: Option C

Explanation

\(\sqrt{2} + \sqrt{32} - 3\sqrt{18} = x\sqrt{8}\)

= \(\sqrt{36 \times 2} + \sqrt{16 \times 2} - 3\sqrt{2 \times 9}\)

= x\(\sqrt{2 \times 4}\)

= 6\(\sqrt{2} + 4\sqrt{2} - 9\sqrt{2} = 2 \times \sqrt{2}\)

\(\sqrt{2} (6 + 4 - 9) = 2x\sqrt{2}\)

\(\sqrt{2} = 2x \sqrt{2}\) divide both sides by \(\sqrt{2}\)

\(\frac{\sqrt{2}}{\sqrt{2}} = \frac{ 2x\sqrt{2}}{\sqrt{2}}\)

1 = 2x

2x = 1

x = \(\frac{1}{2}\)

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