What approximate value will come in place of question mark(?) in the questions given below?
`sqrt9028=?`

Options

A. 45
B. 125
C. 145
D. 95

Answer

To find the approximate value of \( \sqrt{9028} \), we can follow these steps:

### Step 1: Identify the perfect squares near 9028
First, we need to find two perfect squares that are close to 9028. We know that:
- \( 90^2 = 8100 \)
- \( 95^2 = 9025 \)
- \( 100^2 = 10000 \)

From this, we can see that \( 95^2 = 9025 \) is very close to 9028.

### Step 2: Calculate the square root
Since \( 9028 \) is slightly greater than \( 9025 \), we can estimate that \( \sqrt{9028} \) is slightly greater than 95.

### Step 3: Refine the approximation
To refine our approximation, we can calculate:
- \( 95.1^2 = 9051.01 \) (which is greater than 9028)
- \( 95.05^2 = 9040.0025 \) (which is also greater than 9028)
- \( 95.02^2 = 9040.0004 \) (still greater)
- \( 95.01^2 \approx 9001.0001 \) (which is less than 9028)

Since \( 95^2 = 9025 \) and \( 95.01^2 \) is less than 9028, we can conclude that \( \sqrt{9028} \) is approximately \( 95.01 \).

### Step 4: Round off the value
Since we need an approximate value, we can round \( 95.01 \) to \( 95 \).

### Conclusion
Thus, the approximate value of \( \sqrt{9028} \) is \( 95 \).

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