Approximate using perfect squares. Identify the two integers the number is between. Show your work. 78 squared
To approximate the square of 78 using perfect squares, we can find the two perfect squares that 78 falls between.
The perfect square below 78 is 64 (8 squared), and the perfect square above 78 is 81 (9 squared).
Therefore, 78 squared is approximately between 64 squared and 81 squared.
64 squared = 64 * 64 = 4096
81 squared = 81 * 81 = 6561
So, 78 squared is approximately between 4096 and 6561.
To approximate 78 squared using perfect squares, we can find the perfect squares that are closest to 78.
Let's start by finding the perfect squares around 78:
√64 = 8
√81 = 9
The perfect squares closest to 78 are 64 and 81.
Since 78 is between these two squares, we can say that 78 squared is between 64 squared and 81 squared.
64 squared = 64 * 64 = 4096
81 squared = 81 * 81 = 6561
Therefore, 78 squared is between 4096 and 6561.