What does a lower perfect square and a upper perfect square mean.
A lower perfect square refers to a perfect square that is smaller or equal to a given number, while an upper perfect square refers to a perfect square that is larger or equal to a given number.
To understand this concept further, let's start by explaining what a perfect square is. A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a perfect square because it can be written as 2 x 2, giving 2^2 = 4. Similarly, 9 is a perfect square because it can be written as 3 x 3, giving 3^2 = 9.
Now, suppose we have a given number, let's say 14. To find the lower perfect square, we need to look for the perfect square that is smaller or equal to 14. In this case, the lower perfect square is 9 (3 x 3), as it is the largest perfect square that is not greater than 14.
On the other hand, to find the upper perfect square, we need to look for the perfect square that is larger or equal to 14. In this case, the upper perfect square is 16 (4 x 4), as it is the smallest perfect square that is not smaller than 14.
To summarize, a lower perfect square is the largest perfect square smaller or equal to a given number, while an upper perfect square is the smallest perfect square larger or equal to a given number.
A perfect square is a number that can be expressed as the square of an integer.
A lower perfect square refers to the square of the largest integer smaller than a given number.
For example, if we consider the number 16, the largest integer smaller than it is 4. The square of 4 is 16, so 16 is a lower perfect square.
On the other hand, an upper perfect square refers to the square of the smallest integer larger than a given number.
Using the same example, the smallest integer larger than 16 is 5. The square of 5 is 25, so 25 is an upper perfect square.
In general, a lower perfect square is always less than the given number, while an upper perfect square is always greater than the given number.