Find the Least Number to Subtract from 7577 for a Perfect Square

To find the least number that must be subtracted from 7577 to get a perfect square, we need to identify the largest perfect square that is less than 7577.

Step 1: Estimate the Square Root

First, let's estimate the square root of 7577. We know that:

• $80^2 = 6400$
• $90^2 = 8100$

Since 7577 is between 6400 and 8100, its square root is between 80 and 90. Let's try squaring numbers closer to the value.

Calculating the square root:

$\sqrt{7577} \approx 87.0459...$

Step 2: Identify the Largest Lower Perfect Square

The integer part of the square root is 87. Therefore, the largest perfect square less than 7577 is the square of 87.

Calculate $87^2$:

$87^2 = 7569$

This means 7569 is the largest perfect square that is smaller than 7577.

Step 3: Calculate the Number to Subtract

To find the least number that must be subtracted from 7577 to obtain this perfect square (7569), we calculate the difference:

Number to subtract = Given Number - Largest Lower Perfect Square

Number to subtract = $7577 - 7569$

Number to subtract = $8$

Conclusion

The least number that must be subtracted from 7577 to get a perfect square is 8. Subtracting 8 from 7577 gives 7569, which is $87^2$.