Introduction:
To find the least six-digit number which is a perfect square, we need to understand the concept of perfect squares and the properties associated with them. A perfect square is a number that can be expressed as the square of an integer. For example, 4, 9, 16, and 25 are perfect squares because they can be written as 2², 3², 4², and 5² respectively.

Method:
To find the least six-digit number that is a perfect square, we can start by finding the square root of the smallest six-digit number, which is 100,000. The square root of 100,000 is approximately 316.2278. Since the square of any number greater than 316 will be greater than 100,000, we can conclude that the least six-digit perfect square will be less than or equal to 316.

Finding the perfect square:
We can start by squaring the number 316, which gives us 99,856. Since this number is less than 100,000, it is not a six-digit number. Therefore, we need to find the next perfect square.

Incrementing to find the next perfect square:
To find the next perfect square, we can increment our number by 1 and square it. Squaring 317 gives us 100,489, which is greater than 100,000. Therefore, we can conclude that the least six-digit perfect square is the square of 316, which is 99,856.

Conclusion:
The least six-digit number that is a perfect square is 99,856. This number is obtained by squaring the integer 316.

100489