Problem 55 - Elementary Algebra

Question

Determine each of the values, \((|-6|+|4|)^{2}\)

Step-by-Step Solution

Answer

Question: Determine the value of the expression \((|-6|+|4|)^{2}\). Answer: The value of the expression \((|-6|+|4|)^{2}\) is 100.

Step 1: Calculate the absolute values

Firstly, find the absolute value of each number. The absolute value of a number is the distance of the number from zero on the number line, or its non-negative value: \(|-6| = 6\) \(|4| = 4\)

Step 2: Add the absolute values

Now, add the absolute values: \(6 + 4 = 10\)

Step 3: Square the sum

Finally, square the sum of the absolute values: \((10)^{2} = 100\)

Step 4: Final Answer

The value of the expression \((|-6|+|4|)^{2}\) is 100.

Key Concepts

Squared Numbers

When we talk about squared numbers, we are dealing with a number multiplied by itself. In mathematical terms, this is represented as \(n^2\). For example, when we say "10 squared," we mean \(10 \times 10\), which equals 100. Squaring a number is a form of exponentiation, where the exponent is 2. It's a common mathematical operation that is helpful in areas such as geometry, algebra, and various real-life applications.

Doing this step-by-step allows us to thoroughly grasp the concept. Just remember that when you see something like \((10)^{2}\), it means multiply 10 by itself to get the squared number, which in this case is 100.

Addition

Addition is a fundamental operation in math, symbolized by the plus sign \(+\). It involves finding the total or sum by combining numbers. For instance, if you add 6 and 4, you find how much these two numbers equal when put together, which would be 10.

To perform addition:

• Identify the numbers to be added.
• Combine their values.
• Write down the sum you get from the calculation.

In the context of our problem, after obtaining the absolute values as 6 and 4, these are added to get 10 before moving on to the next steps in the problem, which puts this concept into practice.

Problem Solving

Problem solving in mathematics requires a strategic approach to find the correct solution. It often involves:

• Understanding the problem.
• Identifying what is being asked.
• Devising a plan to solve it.
• Carrying out the steps in that plan meticulously.
• Checking the solution to ensure it is correct.

This structured approach helps in systematically tackling any mathematical dilemma one faces. The problem given here could be broken down by first understanding what needs to be achieved – calculating an expression with absolute values and squaring it. Following through this process ensures an accurate solution.

Algebra

Algebra is a branch of mathematics that deals with symbols and rules for manipulating those symbols. In algebraic expressions, numbers are often represented by letters, and these expressions can be managed just like numerical calculations.

Algebra helps us model real-life problems where we may not know specific numbers but can express relations in happy symbolic forms. Take the expression \((|-6|+|4|)^{2}\) as an example:

• The absolute values \(|-6|\) and \(|4|\) are calculated first.
• The result is then organized into an algebraic sum \(6 + 4 = 10\).
• Once we have clear numeric values, the expression is squared \((10)^{2}\).

Working with such expressions strengthens our ability to logically deduce and calculate precise solutions based on general principles.