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Chapter 8: Problem 26

Simplify the squares and square roots. $$8^{2}$$

Short Answer

Expert verified
64

Step by step solution

01

Identify the problem

The problem requires simplifying the square of the number 8, denoted as 8 squared.
02

Understand squaring

When a number is squared, it is multiplied by itself. Thus, squaring 8 means computing 8 multiplied by 8.
03

Calculate the square

Multiply 8 by 8: \(8 \times 8 = 64\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Squaring numbers
Squaring numbers is a fundamental concept in mathematics. It involves multiplying a number by itself. For example, when we square the number 8, we get:
\(8 \times 8 = 64\)
To square a number, follow these steps:
  • Write down the number.
  • Multiply the number by itself.
  • Write down the result, which is the square of the original number.
The process of squaring applies to any number. For example:
\(5^2 = 5 \times 5 = 25\), \(10^2 = 10 \times 10 = 100\), and even to negative numbers: \( (-3)^2 = (-3) \times (-3) = 9\). Remember, squaring a number always results in a positive value, since the product of two negative numbers is positive.
Basic arithmetic
Basic arithmetic is the branch of mathematics that deals with simple computations, such as addition, subtraction, multiplication, and division. In our exercise, we're focused on multiplication, a core arithmetic operation.
When squaring a number, we use multiplication. For instance, in the problem \(8^2\), we multiply 8 by itself.
Suppose we need to simplify \(4^2\):
  • First, identify that we need to multiply the number (4) by itself.
  • Next, perform the multiplication: \(4 \times 4 = 16\).
  • Now, write down the result: \(16\) is the square of \(4\).
Mastering basic arithmetic helps make tasks like squaring numbers much easier.
Mathematical operations
Mathematical operations are the procedures we use to perform calculations. These operations include addition, subtraction, multiplication, and division. In the context of squaring, the operation we use is multiplication.
To better understand multiplication for squaring, consider these points:
  • Multiplication is essentially repeated addition.
  • For example, \(3 \times 3\) is the same as adding 3 three times: \(3 + 3 + 3 = 9\).
  • The symbol \( \times \) denotes multiplication.
When squaring a number, use the multiplication operation:
  • Write the number you need to square.
  • Use the multiplication symbol to indicate the number is multiplied by itself.
  • Solve the multiplication to find the square.
For example, squaring 6 involves multiplying 6 by itself:
\(6^2 = 6 \times 6 = 36\)
Understanding mathematical operations like multiplication is crucial for simplifying squares and other mathematical tasks.

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