The least six digit number which is a perfect square is

Options

A. 100489
B. 100000
C. 100256
D. 100225

Answer

To find the least six-digit number that is a perfect square, we can follow these steps:

### Step 1: Identify the smallest six-digit number
The smallest six-digit number is 100000.

### Step 2: Calculate the square root of the smallest six-digit number
To find the perfect square, we need to calculate the square root of 100000.

\[ \sqrt{100000} = \sqrt{10^5} = 10^{5/2} = 10^{2.5} = 100 \times \sqrt{10} \]

### Step 3: Approximate the value of \(\sqrt{10}\)
The approximate value of \(\sqrt{10}\) is about 3.16.

Now we can calculate:

\[ 100 \times \sqrt{10} \approx 100 \times 3.16 = 316 \]

### Step 4: Find the smallest integer greater than or equal to 316
Since we need a perfect square, we round up to the nearest whole number, which is 316.

### Step 5: Calculate the perfect square of 316
Now we calculate the square of 316:

\[ 316^2 = 99856 \]

This is still a five-digit number. Therefore, we need to check the next integer.

### Step 6: Check the next integer, 317
Now we calculate the square of 317:

\[ 317^2 = 100489 \]

### Step 7: Verify if 100489 is a six-digit number
100489 is indeed a six-digit number and is a perfect square.

### Conclusion
Thus, the least six-digit number which is a perfect square is:

\[ \boxed{100489} \]

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