Find the square root of :
(i) `(1764)/(2809)`
(ii) `(507)/(4107)`
(iii) `sqrt(108 xx 2028)`
(iv) `0.01 + sqrt(0.0064)`

Answer

Let's solve the given problems step by step:

### (i) Find the square root of \(\frac{1764}{2809}\)

1. **Find the square root of the numerator (1764)**:
- The prime factorization of 1764 is \(42^2\).
- Therefore, \(\sqrt{1764} = 42\).

2. **Find the square root of the denominator (2809)**:
- The prime factorization of 2809 is \(53^2\).
- Therefore, \(\sqrt{2809} = 53\).

3. **Combine the results**:
\[ \sqrt{\frac{1764}{2809}} = \frac{\sqrt{1764}}{\sqrt{2809}} = \frac{42}{53} \]

**Final Answer**: \(\frac{42}{53}\)