Find the square of :
(i) `(3sqrt(5))/5" (ii) "3+2sqrt(5)`

Answer

Let's solve the question step by step.

### Question:
Find the square of:
(i) \(\frac{3\sqrt{5}}{5}\)
(ii) \(3 + 2\sqrt{5}\)

### Solution:

#### Part (i): Find the square of \(\frac{3\sqrt{5}}{5}\)

1. **Write the expression**:
\[ \left(\frac{3\sqrt{5}}{5}\right)^2 \]

2. **Square the numerator and the denominator**:
\[ = \frac{(3\sqrt{5})^2}{5^2} \]

3. **Calculate the square of the numerator**:
- The square of \(3\) is \(9\).
- The square of \(\sqrt{5}\) is \(5\).
\[ (3\sqrt{5})^2 = 3^2 \cdot (\sqrt{5})^2 = 9 \cdot 5 = 45 \]

4. **Calculate the square of the denominator**:
\[ 5^2 = 25 \]

5. **Combine the results**:
\[ = \frac{45}{25} \]

6. **Simplify the fraction**:
- Both \(45\) and \(25\) can be divided by \(5\).
\[ = \frac{9}{5} \]

7. **Convert to a mixed number (optional)**:
\[ = 1 \frac{4}{5} \]

#### Part (ii): Find the square of \(3 + 2\sqrt{5}\)

1. **Write the expression**:
\[ (3 + 2\sqrt{5})^2 \]

2. **Apply the identity \((a + b)^2 = a^2 + 2ab + b^2\)**:
- Let \(a = 3\) and \(b = 2\sqrt{5}\).
\[ = 3^2 + 2 \cdot 3 \cdot (2\sqrt{5}) + (2\sqrt{5})^2 \]

3. **Calculate each term**:
- \(3^2 = 9\)
- \(2 \cdot 3 \cdot (2\sqrt{5}) = 12\sqrt{5}\)
- \((2\sqrt{5})^2 = 4 \cdot 5 = 20\)

4. **Combine the results**:
\[ = 9 + 12\sqrt{5} + 20 \]

5. **Simplify**:
\[ = 29 + 12\sqrt{5} \]

### Final Answers:
(i) \(\frac{9}{5}\) or \(1 \frac{4}{5}\)
(ii) \(29 + 12\sqrt{5}\)