Is 16×2 24×9 a perfect square? This question often arises in mathematical discussions and can be answered by examining the properties of perfect squares and the structure of the given expression. In this article, we will explore the concept of perfect squares, analyze the given expression, and determine whether it is indeed a perfect square.
A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it can be written as 4^2, and 25 is a perfect square because it can be written as 5^2. To determine if a number is a perfect square, we can check if its square root is an integer.
Now, let’s analyze the given expression, 16×2 24×9. This expression can be simplified by multiplying the numbers within the parentheses. Thus, we have:
16×2 = 32
24×9 = 216
Now, we can rewrite the expression as:
32 + 216
To determine if this sum is a perfect square, we need to find its square root. The square root of 32 is approximately 5.6569, and the square root of 216 is approximately 14.7968. Since neither of these square roots is an integer, we can conclude that 32 + 216 is not a perfect square.
In conclusion, the expression 16×2 24×9 is not a perfect square. This is because the sum of the simplified expression, 32 + 216, does not have an integer square root. Understanding the properties of perfect squares and how to determine them is an essential skill in mathematics, and this example demonstrates the process of analyzing an expression to determine its nature.
