Problem 92 - Prealgebra

Question

The problems below review some of the material on solving equations. Reviewing these problems will help you with the next section. Solve. $$(2.1)^{2}$$

Step-by-Step Solution

Answer

The square of 2.1 is 4.41.

Step 1: Identify the Operation

The problem requires squaring the number 2.1. Squaring means multiplying the number by itself.

Step 2: Set Up the Multiplication

Express the square of 2.1 as a multiplication problem: \( (2.1)^2 = 2.1 imes 2.1 \).

Step 3: Perform the Multiplication

Now, multiply 2.1 by 2.1. You can do this as follows: First, multiply 1 by 1, which equals 1. Next, multiply 1 by 0.2 (from the other 2.1), and the result is 0.2. Then, multiply 2 by 1, resulting in 2. Finally, multiply 2 by 0.2, which equals 0.4. Add all these results together: 1 + 0.2 + 2 + 0.4 = 4.41. This can also be done by using a calculator to directly compute 2.1 squared.

Step 4: Finalize the Answer

After performing the multiplication, the square of 2.1 is 4.41. So, \( (2.1)^2 = 4.41 \).

Key Concepts

Solving Equations

Solving equations is an essential part of prealgebra, and it often involves finding the value of an unknown variable that makes the equation true. When faced with an equation, the goal is to isolate the variable, usually on one side of the equation, so its value can be determined.One important step in solving equations is understanding the operations that are involved. These might include addition, subtraction, multiplication, or division. It's important to perform the same operation on both sides of the equation to maintain balance and equality. Often, operations are reversed to isolate the variable, such as adding when the equation involves subtraction, and vice versa.For example, if an equation is: \[x + 5 = 10\]You would subtract 5 from both sides to solve for \(x\):\[x = 10 - 5 = 5\]Being methodical and patient while managing each operation ensures the equation is simplified correctly, leading to an accurate solution.

Squaring Numbers

Squaring a number means multiplying it by itself. In mathematical terms, the square of a number is expressed as \(n^2\), where \(n\) is any real number. In our exercise, this is demonstrated with the number 2.1.Squaring can be approached with a few simple steps:

• Multiply the number by itself.
• Simplify the multiplication by breaking it down, especially when dealing with decimals or complex numbers.

For the number 2.1, the multiplication is set up as \((2.1 \times 2.1)\). The multiplication is broken into manageable parts:- Multiply the whole numbers, then consider decimal places.- Add the results to find the final value.This method allows for accurate calculation even when done manually. Advanced tools, like a calculator, can also immediately square numbers, reducing the time for computation and ensuring precision.

Step-by-Step Solutions

Step-by-step solutions are invaluable for understanding mathematics, especially in prealgebra. They break down complex problems into comprehensible parts, allowing students to follow the logic and methodology used at each stage. When solving a problem like squaring a number, here's how step-by-step solutions help:

• Begins with identifying the mathematical operation involved, such as squaring.
• Illustrates setting up the equation for multiplication, thereby clarifying the operation.
• Provides detailed multiplication steps, showing each part of the calculation separately.
• Keeps the process organized, making it easier to spot errors and verify results.

By explaining each part of the process, step-by-step solutions enhance comprehension and learning retention. They allow students to easily replicate the process independently and become more confident in tackling various math problems.