((√(2) - 2) - (1 ÷ 2)) ÷ (1 ÷ 2)
You asked:
Evaluate the expression: \(\frac{\sqrt{2} - 2 - \frac{1}{2}}{\frac{1}{2}}\)
MathBot Answer:
\[\frac{\sqrt{2} - 2 - \frac{1}{2}}{\frac{1}{2}} = -5 + 2 \sqrt{2} \approx -2.1715728752538099023966225515806\]
\[\begin{aligned}\frac{\sqrt{2} - 2 - \frac{1}{2}}{\frac{1}{2}}& = \left(\sqrt{2} - 2 - \frac{1}{2}\right) \cdot \frac{1}{\frac{1}{2}}\\& = \left(\left(-2 + \sqrt{2}\right) - \frac{1}{2}\right) \cdot \frac{1}{\frac{1}{2}}\\& = \left(- \frac{5}{2} + \sqrt{2}\right) \cdot \frac{1}{\frac{1}{2}}\\& = -5 + 2 \cdot \sqrt{2}\end{aligned}\]