Question: User: $\frac{1}{4} = \frac{4}{0.8} + \sqrt{0.8 + 0.2} - 5 \times 0.3$
1. **State the problem:**
We need to verify or simplify the equation $$\frac{1}{4} = \frac{4}{0.8} + \sqrt{0.8 + 0.2} - 5 \times 0.3$$
2. **Calculate each term on the right side:**
- Calculate $$\frac{4}{0.8}$$:
$$\frac{4}{0.8} = \frac{4}{\cancel{0.8}} \times \frac{1}{\cancel{0.8}} = 5$$
- Calculate the square root term $$\sqrt{0.8 + 0.2}$$:
$$0.8 + 0.2 = 1.0$$
$$\sqrt{1.0} = 1$$
- Calculate $$5 \times 0.3$$:
$$5 \times 0.3 = 1.5$$
3. **Substitute the values back into the right side:**
$$5 + 1 - 1.5 = 6 - 1.5 = 4.5$$
4. **Compare both sides:**
Left side is $$\frac{1}{4} = 0.25$$
Right side is $$4.5$$
5. **Conclusion:**
The equation $$\frac{1}{4} = \frac{4}{0.8} + \sqrt{0.8 + 0.2} - 5 \times 0.3$$ is false because $$0.25 \neq 4.5$$.