Find the least number which if added to 17420 will make it a perfect square?

Options

A. 3
B. 5
C. 9
D. 4

Answer

To find the least number which, when added to 17420, will make it a perfect square, we can follow these steps:

### Step 1: Identify the number
We need to find the least number \( x \) such that \( 17420 + x \) is a perfect square.

### Step 2: Estimate the square root
First, we will estimate the square root of 17420. We can find the nearest perfect squares around this number.

Calculating the square root:
\[ \sqrt{17420} \approx 132 \]
because \( 132^2 = 17424 \) and \( 131^2 = 17161 \).

### Step 3: Calculate the perfect square
Now, we calculate \( 132^2 \):
\[ 132^2 = 17424 \]

### Step 4: Find the difference
Next, we find the difference between 17424 and 17420:
\[ 17424 - 17420 = 4 \]

### Step 5: Conclusion
Thus, the least number that needs to be added to 17420 to make it a perfect square is:
\[ \boxed{4} \]

---