What approximate value should come in the following question mark (?) (You are not expected to calculate the exact value )
`sqrt1000 = ?`

Options

A. 10
B. 24
C. 45
D. 32

Answer

To find the approximate value of \(\sqrt{1000}\), we can follow these steps:

### Step 1: Break down 1000
We can express 1000 as a product of simpler numbers.
\[ 1000 = 100 \times 10 \]

### Step 2: Calculate the square root of 100
Next, we find the square root of 100.
\[ \sqrt{100} = 10 \]

### Step 3: Rewrite the square root of 1000
Now, we can rewrite the square root of 1000 using the result from Step 2:
\[ \sqrt{1000} = \sqrt{100 \times 10} = \sqrt{100} \times \sqrt{10} = 10 \times \sqrt{10} \]

### Step 4: Estimate \(\sqrt{10}\)
To estimate \(\sqrt{10}\), we can note that it lies between the square roots of 9 and 16:
\[ \sqrt{9} = 3 \quad \text{and} \quad \sqrt{16} = 4 \]
Thus, \(\sqrt{10}\) is approximately between 3 and 4. A closer approximation is around 3.2.

### Step 5: Multiply by 10
Now, we multiply our approximation of \(\sqrt{10}\) by 10:
\[ 10 \times \sqrt{10} \approx 10 \times 3.2 = 32 \]

### Conclusion
Therefore, the approximate value of \(\sqrt{1000}\) is:
\[ \sqrt{1000} \approx 32 \]

### Final Answer
The answer is 32.

---