The square root of a certain number is approximately 9.2371. The certain number is between what 2 intergers?

Options

A. 3 and 4
B. 4 and 5
C. 9 and 10
D. 81 and 99

Answer

To find the two integers between which the certain number \( x \) lies, we start with the given information that the square root of \( x \) is approximately \( 9.2371 \).

### Step 1: Set up the equation
Let \( x \) be the certain number. According to the problem, we have:
\[ \sqrt{x} \approx 9.2371 \]

### Step 2: Square both sides
To eliminate the square root, we square both sides of the equation:
\[ x \approx (9.2371)^2 \]

### Step 3: Calculate the square
Now we calculate \( (9.2371)^2 \):
\[ (9.2371)^2 \approx 85.32401641 \]

### Step 4: Identify the range of integers
Now that we have \( x \approx 85.32401641 \), we need to find the two integers between which this value lies. The integers immediately surrounding \( 85.32401641 \) are \( 85 \) and \( 86 \).

### Step 5: Conclusion
Thus, we can conclude that the certain number \( x \) is between the integers \( 85 \) and \( 86 \).

### Final Answer
The certain number is between the integers **85 and 86**.

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