The least number that must be subtracted from 63520 to make the result a perfect square is

Options

A. 30
B. 24
C. 14
D. 16

Answer

To find the least number that must be subtracted from 63520 to make it a perfect square, we can follow these steps:

### Step 1: Find the square root of 63520
First, we need to estimate the square root of 63520. We can find the nearest whole number whose square is close to 63520.

Calculating:
- \( 250^2 = 62500 \)
- \( 260^2 = 67600 \)

Since \( 62500 < 63520 < 67600 \), we can conclude that the square root of 63520 is between 250 and 260.

### Step 2: Check the perfect squares around the estimated square root
Next, we will check the perfect squares of the integers between 250 and 260 to see which one is closest to 63520.

Calculating:
- \( 251^2 = 63001 \)
- \( 252^2 = 63504 \)
- \( 253^2 = 64009 \)

### Step 3: Identify the closest perfect square
From the calculations:
- \( 63001 \) is less than \( 63520 \)
- \( 63504 \) is very close to \( 63520 \)
- \( 64009 \) is greater than \( 63520 \)

The closest perfect square less than \( 63520 \) is \( 63504 \).

### Step 4: Calculate the difference
Now, we need to find the difference between \( 63520 \) and \( 63504 \):

\[ 63520 - 63504 = 16 \]

### Conclusion
The least number that must be subtracted from \( 63520 \) to make it a perfect square is \( 16 \).