Find the difference in 777 and its nearest perfect square number.

Options

A. 4
B. 7
C. 27
D. 28

Answer

To find the difference between 777 and its nearest perfect square number, follow these steps:

### Step 1: Identify the perfect squares around 777
- First, we need to find the square root of 777 to determine which perfect squares are near it.
- The square root of 777 is approximately 27.86.

### Step 2: Calculate the perfect squares of the integers around the square root
- The perfect square of 27 is \(27^2 = 729\).
- The perfect square of 28 is \(28^2 = 784\).

### Step 3: Determine the nearest perfect square
- Now, we compare the two perfect squares we calculated:
- 729 (which is less than 777)
- 784 (which is greater than 777)
- Since 777 is closer to 784 than it is to 729, the nearest perfect square to 777 is 784.

### Step 4: Calculate the difference
- Now, we find the difference between 777 and the nearest perfect square (784):
\[ 784 - 777 = 7 \]

### Final Answer
- The difference between 777 and its nearest perfect square number is **7**.

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