For the two given questions I and II
`p = sqrt 4/ sqrt 9`
`9q^2 – 12q + 4 = 0`

Options

A. if p is greater than q.
B. if p is smaller than q
C. if p is equal to q
D. if p is either equal to or smaller than q

Answer

To solve the given questions step by step, let's break it down:

### Question I: Calculate p
1. **Expression for p**:
\[ p = \frac{\sqrt{4}}{\sqrt{9}} \]

2. **Calculate \(\sqrt{4}\)**:
\[ \sqrt{4} = 2 \]

3. **Calculate \(\sqrt{9}\)**:
\[ \sqrt{9} = 3 \]

4. **Substituting the values back into the expression for p**:
\[ p = \frac{2}{3} \]

### Question II: Solve the quadratic equation for q
1. **Given equation**:
\[ 9q^2 - 12q + 4 = 0 \]

2. **Identify coefficients**:
- \(a = 9\)
- \(b = -12\)
- \(c = 4\)

3. **Use the quadratic formula**:
\[ q = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

4. **Calculate \(b^2 - 4ac\)**:
\[ b^2 = (-12)^2 = 144 \]
\[ 4ac = 4 \cdot 9 \cdot 4 = 144 \]
\[ b^2 - 4ac = 144 - 144 = 0 \]

5. **Substituting into the quadratic formula**:
\[ q = \frac{-(-12) \pm \sqrt{0}}{2 \cdot 9} \]
\[ q = \frac{12 \pm 0}{18} \]
\[ q = \frac{12}{18} = \frac{2}{3} \]

### Summary of Results
- The value of \(p\) is \(\frac{2}{3}\).
- The value of \(q\) is also \(\frac{2}{3}\).

### Comparison of p and q
- Since \(p = \frac{2}{3}\) and \(q = \frac{2}{3}\), we conclude that \(p\) is equal to \(q\).

### Final Answer
- Both \(p\) and \(q\) are equal to \(\frac{2}{3}\).