What approximate value should come in place of question mark (?) in the following questions ? (Note: You are not expected to calculate the exact value)
`sqrt(2230)`= ?

Options

A. 54
B. 59
C. 41
D. 47

Answer

To find the approximate value of \( \sqrt{2230} \), we will follow these steps:

### Step 1: Identify the perfect squares around 2230
First, we need to find two perfect squares that are close to 2230. The perfect squares we consider are:
- \( 44^2 = 1936 \)
- \( 45^2 = 2025 \)
- \( 46^2 = 2116 \)
- \( 47^2 = 2209 \)
- \( 48^2 = 2304 \)

From this, we can see that \( 47^2 = 2209 \) is less than 2230, and \( 48^2 = 2304 \) is greater than 2230.

### Step 2: Determine the approximate value
Since \( 2230 \) is between \( 47^2 \) and \( 48^2 \), we can conclude that:
\[ 47 < \sqrt{2230} < 48 \]

### Step 3: Estimate the value
To get a more precise approximation, we can calculate how far 2230 is from 2209 and 2304:
- The difference between \( 2230 \) and \( 2209 \) is \( 2230 - 2209 = 21 \).
- The difference between \( 2304 \) and \( 2230 \) is \( 2304 - 2230 = 74 \).

Since \( 2230 \) is closer to \( 2209 \) than to \( 2304 \), we can estimate that \( \sqrt{2230} \) is closer to \( 47 \).

### Step 4: Final approximation
Given that \( 2230 \) is much closer to \( 2209 \) than to \( 2304 \), we can approximate:
\[ \sqrt{2230} \approx 47.5 \]

Since we are looking for an approximate integer value, we can round it down to \( 47 \).

### Conclusion
Thus, the approximate value that should come in place of the question mark (?) is:
\[ \sqrt{2230} \approx 47 \]

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