Which of the number `-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 evaluate each number and compare it with its square.

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

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

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

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

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