Using differentials, find the approximate value of each of the following up to 3 places of decimal.(i) `sqrt(25. 3)` (ii) `sqrt(49. 5)` (iii) `sqrt(0. 6)` (iv) `(0. 009)^(1/3)` (v) `(0. 999)^(1/(10))`(vi) `(15)^(1/4)`

Explanation

To find the approximate values using differentials, we will follow the steps outlined in the video transcript. Let's solve each part step by step.

### (i) Approximate value of `sqrt(25.3)`

1. **Choose a value for x**: Let \( x = 25 \).
2. **Calculate \( \sqrt{x} \)**: \( \sqrt{25} = 5 \).
3. **Determine change in x**: \( \Delta x = 25.3 - 25 = 0.3 \).
4. **Define y**: Let \( y = \sqrt{x} \).
...