what is a perfect square number i know 9, 25 and 100, but what else
if you multiply a perfect square by a perfect square, is the answer always a perfect square
Yes, this might be easier to understand if you think of expressing the perfect square as a product of its square roots. Rearrange to see that the product is a perfect square
if x and y are perfect squares:
x = a * a
y = b * b
x * y = a * a * b * b
x * y = (a * b) * (a * b)
let c = a * b
x * y = c * c
A perfect square is a number that can be expressed as the square of an integer. In addition to 9, 25, and 100, there are many more perfect square numbers. Here are a few examples:
- 16 is a perfect square because it can be expressed as 4 * 4.
- 36 is a perfect square because it can be expressed as 6 * 6.
- 64 is a perfect square because it can be expressed as 8 * 8.
- 121 is a perfect square because it can be expressed as 11 * 11.
- 144 is a perfect square because it can be expressed as 12 * 12.
Regarding your second question, if you multiply two perfect squares together, then the result will always be a perfect square. This is because when you multiply the squares of two integers (perfect squares), you are essentially multiplying the integer by itself twice, which is the definition of a perfect square.
A perfect square number is a number that can be obtained by multiplying an integer by itself. For example, 9 is a perfect square because 3 multiplied by 3 equals 9.
To find more perfect square numbers, you can continue squaring integers. Here are some other examples:
- 16 is a perfect square because 4 multiplied by 4 equals 16.
- 36 is a perfect square because 6 multiplied by 6 equals 36.
- 49 is a perfect square because 7 multiplied by 7 equals 49.
- 64 is a perfect square because 8 multiplied by 8 equals 64.
- And so on...
Now, let's answer your second question. If you multiply two perfect square numbers together, the result will indeed always be a perfect square. This can be easily demonstrated using algebra.
Let's say you have two perfect square numbers, m and n. They can be written as m = a^2 and n = b^2, where a and b are integers.
When you multiply m and n together, you get (a^2)(b^2). Using the properties of exponents, you can simplify this expression to (ab)^2.
Therefore, the product of two perfect square numbers is (ab)^2, which means it is also a perfect square.