Simplify the expression (64)2
The Correct Answer and Explanation is :
To simplify the expression ( (64)^2 ), we will perform the calculation directly.
Calculation:
First, we recognize that squaring a number means multiplying that number by itself:
[
(64)^2 = 64 \times 64
]
Now, we can perform the multiplication:
[
64 \times 64 = 4096
]
Conclusion:
Thus, the simplified expression for ( (64)^2 ) is ( 4096 ).
Explanation:
The process of squaring a number is a fundamental concept in mathematics, often encountered in various fields such as arithmetic, algebra, and geometry. When we square a number, we are effectively determining the area of a square whose sides have the length of that number. In this case, if we consider a square with each side measuring 64 units, the area of that square can be found by multiplying the length of one side by itself, which leads us to ( 64 \times 64 ).
To understand why the multiplication results in ( 4096 ), we can break it down further using the properties of numbers. One way to approach this multiplication is by using the distributive property. We can express ( 64 ) as ( 60 + 4 ):
[
64 \times 64 = (60 + 4)(60 + 4)
]
Using the distributive property (also known as the FOIL method in binomials), we get:
[
= 60^2 + 2 \times 60 \times 4 + 4^2
]
Calculating each term separately:
[
60^2 = 3600
]
[
2 \times 60 \times 4 = 480
]
[
4^2 = 16
]
Now, adding these results together:
[
3600 + 480 + 16 = 4096
]
This breakdown confirms that ( (64)^2 ) indeed equals ( 4096 ). Understanding the squaring process and the properties of numbers allows for various methods to arrive at the same result, reinforcing the foundational principles of multiplication and area in mathematics.