If `sqrt(784) = 28`, find the value of :
(i) `sqrt(7.84) + sqrt(78400)`
(ii) `sqrt(0.0784) + sqrt(0.000784)`

Answer

To solve the given problem, we will break it down into two parts as specified in the question.

### Part (i): Find the value of `sqrt(7.84) + sqrt(78400)`

1. **Calculate `sqrt(7.84)`**:
- We know that `sqrt(784) = 28`.
- Since `7.84` can be expressed as `784 / 100`, we can use the property of square roots:
\[ \sqrt{7.84} = \sqrt{\frac{784}{100}} = \frac{\sqrt{784}}{\sqrt{100}} = \frac{28}{10} = 2.8 \]

2. **Calculate `sqrt(78400)`**:
- We can express `78400` as `784 * 100`.
- Using the property of square roots:
\[ \sqrt{78400} = \sqrt{784 \times 100} = \sqrt{784} \times \sqrt{100} = 28 \times 10 = 280 \]

3. **Add the two results**:
\[ \sqrt{7.84} + \sqrt{78400} = 2.8 + 280 = 282.8 \]

### Part (ii): Find the value of `sqrt(0.0784) + sqrt(0.000784)`

1. **Calculate `sqrt(0.0784)`**:
- We can express `0.0784` as `784 / 10000`.
- Using the property of square roots:
\[ \sqrt{0.0784} = \sqrt{\frac{784}{10000}} = \frac{\sqrt{784}}{\sqrt{10000}} = \frac{28}{100} = 0.28 \]

2. **Calculate `sqrt(0.000784)`**:
- We can express `0.000784` as `784 / 1000000`.
- Using the property of square roots:
\[ \sqrt{0.000784} = \sqrt{\frac{784}{1000000}} = \frac{\sqrt{784}}{\sqrt{1000000}} = \frac{28}{1000} = 0.028 \]

3. **Add the two results**:
\[ \sqrt{0.0784} + \sqrt{0.000784} = 0.28 + 0.028 = 0.308 \]

### Final Answers:
- (i) `sqrt(7.84) + sqrt(78400) = 282.8`
- (ii) `sqrt(0.0784) + sqrt(0.000784) = 0.308`