Which number is a perfect square? 249 or 256
The correct answer and explanation is:
Correct Answer: 256
A perfect square is a number that can be expressed as the product of an integer multiplied by itself. In mathematical terms, if n is an integer and n × n = x, then x is called a perfect square.
Let us examine both numbers:
256 is equal to 16 multiplied by 16. That is:
16 × 16 = 256
This means 256 is a perfect square because it is the square of the integer 16.
On the other hand, 249 is not a perfect square. If we try squaring integers near the square root of 249, we find:
15 × 15 = 225
16 × 16 = 256
This shows that 249 lies between two perfect squares, 225 and 256. Since there is no whole number that, when squared, equals 249, it cannot be considered a perfect square.
Perfect squares have distinct properties. They always have an odd number of total factors, and their square roots are always integers. These numbers also appear frequently in algebra, geometry, and number theory. Recognizing perfect squares is useful in simplifying square roots, solving quadratic equations, and working with areas of squares in geometry.
The square root of 256 is exactly 16, which is an integer, so 256 satisfies the definition of a perfect square. Meanwhile, the square root of 249 is approximately 15.78, which is not an integer. Therefore, 249 does not qualify.
In conclusion, 256 is the perfect square between the two numbers because it is the square of the whole number 16.