If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m.
A. \(1\frac{1}{2}\)
B. \(1\frac{1}{4}\)
C. \(2\frac{1}{4}\)
D. \(2\frac{1}{2}\)
Correct Answer: C
Explanation
\(\frac{5}{\sqrt{2}} = \frac{5 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{5\sqrt{2}}{2}\)
\(\frac{\sqrt{8}}{8} = \frac{2\sqrt{2}}{8} = \frac{\sqrt{2}}{4}\)
\(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = (\frac{5}{2} - \frac{1}{4})\sqrt{2}\)
= \(\frac{9}{4}\sqrt{2} \)
= \(2\frac{1}{4}\sqrt{2}\)
