Which of the following numbers is a perfect square?a209 b1 000c1 524 d1 764

The perfect square among the given options is b1 000.

Here's the step by step process:

A perfect square is a number that can be expressed as the product of an integer with itself. For example, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are perfect squares.

Now, let's check each option:

a) 209: The square root of 209 is approximately 14.4568323, which is not an integer. So, 209 is not a perfect square.

b) 1 000: The square root of 1 000 is exactly 31.6227766, which is not an integer. So, 1 000 is not a perfect square.

c) 1 524: The square root of 1 524 is approximately 39.012818, which is not an integer. So, 1 524 is not a perfect square.

d) 1 764: The square root of 1 764 is exactly 42, which is an integer. So, 1 764 is a perfect square.

So, the correct answer is d) 1 764.