Whih of the numbers `-20, -(3)/(4), (1)/(2), 10` is greater than its square ?

Options

A. 10
B. `-20`
C. `(1)/(2)`
D. `-(3)/(4)`

Answer

To determine which of the numbers \(-20\), \(-\frac{3}{4}\), \(\frac{1}{2}\), and \(10\) is greater than its square, we will calculate the square of each number and compare it with the original number.

### Step-by-Step Solution:

1. **Calculate the square of each number:**
- For \(-20\):
\[ (-20)^2 = 400 \]
- For \(-\frac{3}{4}\):
\[ \left(-\frac{3}{4}\right)^2 = \frac{9}{16} \]
- For \(\frac{1}{2}\):
\[ \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]
- For \(10\):
\[ 10^2 = 100 \]

2. **Compare each number with its square:**
- For \(-20\):
\[ -20 < 400 \quad \text{(not greater)} \]
- For \(-\frac{3}{4}\):
\[ -\frac{3}{4} < \frac{9}{16} \quad \text{(not greater)} \]
- For \(\frac{1}{2}\):
\[ \frac{1}{2} > \frac{1}{4} \quad \text{(greater)} \]
- For \(10\):
\[ 10 < 100 \quad \text{(not greater)} \]

3. **Conclusion:**
The only number that is greater than its square is \(\frac{1}{2}\).

### Final Answer:
The number that is greater than its square is \(\frac{1}{2}\).