Problem 95 - Prealgebra

Question

The problems below review some of the material on solving equations. Reviewing these problems will help you with the next section. Solve. $$6^{2}+8^{2}$$

Step-by-Step Solution

Answer

The result of \(6^{2} + 8^{2}\) is 100.

Step 1: Identify the Problem

The exercise asks us to calculate the value of the expression \(6^{2} + 8^{2}\). This involves squaring each number separately and then adding the results.

Step 2: Calculate the Square of 6

To solve \(6^{2}\), we multiply 6 by itself: \(6 \times 6 = 36\). Thus, \(6^{2} = 36\).

Step 3: Calculate the Square of 8

Next, calculate \(8^{2}\) by multiplying 8 by itself: \(8 \times 8 = 64\). Therefore, \(8^{2} = 64\).

Step 4: Add the Results

Finally, add the results of the squares: \(36 + 64 = 100\). The value of the expression is 100.

Key Concepts

Understanding Squaring Numbers

Squaring a number is a fundamental arithmetic operation that is both simple and powerful in various mathematical calculations. When you square a number, you multiply the number by itself.
This concept is important because squares often appear in algebra, geometry, and calculus.

• When you see an expression like \(6^2\), it's telling you to calculate \(6 \times 6\), which gives 36.
• Similarly, \(8^2\) means you multiply 8 by 8, resulting in 64.

Squaring numbers is essential when solving quadratic equations, dealing with Pythagorean theorem problems, or working with exponents.

Mastering Addition

Addition is one of the most basic arithmetic operations and is crucial for building up your math skills. It helps you in combining values, which is essential in solving equations and performing various calculations.
For instance, when you have two results from squaring numbers, like 36 and 64, the next step is to add them.

• Here, 36 + 64 = 100.
• It's crucial to line up numbers correctly, especially with digits of different lengths, to ensure accurate addition.

This operation is straightforward but forms the foundation for more complex operations, such as multiplication and functions.

Exploring Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics. They include addition, subtraction, multiplication, and division. Understanding these operations allows you to solve a wide range of mathematical problems and equations.
In the given problem, you're dealing with squaring numbers and then using addition to find the final result.

• First, you complete the multiplication step in the squaring process: \(6 \times 6\) and \(8 \times 8\).
• Then, you proceed to add these squared numbers: \(36 + 64\).

Being proficient in arithmetic means you can apply these skills effortlessly in more complex mathematics, including algebra and calculus.