Which statement explains why 49 is a perfect square?
In the realm of mathematics, perfect squares hold a unique place as they are the product of an integer multiplied by itself. The number 49, for instance, is a prime example of a perfect square. To understand why 49 is a perfect square, we need to delve into the properties of square numbers and the underlying mathematical principles that govern them.
The first step in understanding why 49 is a perfect square is to recognize that it is the square of an integer. In this case, the integer is 7. The process of squaring a number involves multiplying it by itself. Therefore, 49 can be expressed as 7 multiplied by 7, or 7^2. This means that 49 is the result of an integer (7) being squared, which is the defining characteristic of a perfect square.
Another way to determine if a number is a perfect square is to find its square root. The square root of a number is the value that, when multiplied by itself, gives the original number. For 49, the square root is 7, as 7 multiplied by 7 equals 49. This confirms that 49 is indeed a perfect square, as it has a whole number square root.
In addition to these methods, we can also use the properties of prime numbers to explain why 49 is a perfect square. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. The number 7 is a prime number, and since it is being squared to produce 49, we can conclude that 49 is a perfect square.
In conclusion, the statement that explains why 49 is a perfect square is that it is the square of an integer (7) and has a whole number square root (7). Additionally, the fact that 7 is a prime number further supports the notion that 49 is a perfect square. Understanding these properties helps us appreciate the beauty and simplicity of mathematics and the fascinating world of perfect squares.
