Question: Y/ = 4/0.8 + \sqrt{0.8+0.2} - 5 \times 0.8
1. **State the problem:** We need to evaluate the expression $$Y/ = \frac{4}{0.8} + \sqrt{0.8 + 0.2} - 5 \times 0.8$$.
2. **Recall formulas and rules:**
- Division and multiplication follow standard arithmetic rules.
- The square root function \(\sqrt{x}\) returns the positive root of \(x\).
- Order of operations: parentheses, exponents (including roots), multiplication/division (left to right), addition/subtraction (left to right).
3. **Calculate each part step-by-step:**
- Calculate the division: $$\frac{4}{0.8} = \frac{4}{\cancel{0.8}} \times \frac{\cancel{1}}{1} = 5$$ (since \(0.8 \times 5 = 4\)).
- Calculate inside the square root: $$0.8 + 0.2 = 1.0$$.
- Calculate the square root: $$\sqrt{1.0} = 1$$.
- Calculate the multiplication: $$5 \times 0.8 = 4$$.
4. **Combine all parts:**
$$Y/ = 5 + 1 - 4$$
5. **Simplify the expression:**
$$Y/ = 6 - 4 = 2$$
**Final answer:** $$Y/ = 2$$