Find the least number which must be subtracted from 7581 to obtain a perfect square. Find this perfect square and its square root.

Answer

To solve the problem of finding the least number that must be subtracted from 7581 to obtain a perfect square, we will follow these steps:

### Step 1: Identify the nearest perfect square
First, we need to find the square root of 7581 to determine the nearest perfect square.

Calculating the square root:
\[ \sqrt{7581} \approx 87 \]
Now, we will check the perfect squares of 87 and 88:
\[ 87^2 = 7569 \]
\[ 88^2 = 7744 \]

### Step 2: Determine the closest perfect square
From our calculations:
- \(87^2 = 7569\) (which is less than 7581)
- \(88^2 = 7744\) (which is greater than 7581)

Since we are looking for the least number to subtract, we will consider the perfect square \(7569\).

### Step 3: Calculate the difference
Now, we subtract \(7569\) from \(7581\) to find the least number that must be subtracted:
\[ 7581 - 7569 = 12 \]

### Step 4: Conclusion
The least number that must be subtracted from 7581 to obtain a perfect square is \(12\). The perfect square obtained is \(7569\), and the square root of \(7569\) is \(87\).

### Final Answer:
- Least number to subtract: **12**
- Perfect square: **7569**
- Square root of the perfect square: **87**

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