Problem 50 Find the value of \(a^{2}+b^{2}\... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 7: Problem 50

Find the value of $a^{2}+b^{2}$ for the given values of a and $b$ $$ a=7, b=24 $$

Short Answer

Expert verified

625

Step by step solution

- Square the value of a

Given that $a = 7$, first calculate $a^2$, which is $7^2 $. $7^2 = 49$

- Square the value of b

Given that $b = 24$, next calculate $b^2$, which is $24^2 $. $24^2 = 576$

- Add the squared values

Add the results from Step 1 and Step 2: $49 + 576$. $49 + 576 = 625$

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Key Concepts

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

Squaring Numbers

Squaring a number means multiplying the number by itself. For instance, when we need to find the value of a squared number, we take our number and simply perform the multiplication.
For example, if we have $a = 7$, then to find $a^2$ we multiply 7 by 7. This gives us $7^2 = 49$.
The same process is followed for any number. Consider $b = 24$, squaring b means $24 \times 24 = 576$.
The squaring operation is fundamental in algebra and forms the basis for more complex calculations, such as solving quadratic equations. It's important to remember that squaring always results in a non-negative number, whether the original number is positive or negative.

Addition of Squares

Adding the squares of numbers involves first calculating the square of each number and then performing the addition.
For example, let鈥檚 say you have two numbers, 7 and 24. First, you find the square of each:

$7^2 = 49$
$24^2 = 576$

Then, you simply add these squared values together: $49 + 576 = 625$. This is a straightforward but crucial skill in algebra, often used in solving geometric problems and equations involving the Pythagorean theorem.

Step-by-Step Problem Solving

Step-by-step problem solving is an essential approach in algebra. It helps in understanding and organizing the process to find the correct answer, breaking down complex problems into manageable steps.
Let's revisit our example problem for clarity. We want to find the value of $a^2 + b^2$ where $a = 7$ and $b = 24$.

Step 1: Calculate $a^2$. Given $a = 7$, we get $a^2 = 7^2 = 49$.
Step 2: Calculate $b^2$. Given $b = 24$, we get $b^2 = 24^2 = 576$.
Step 3: Add $a^2$ and $b^2$. Thus, $49 + 576 = 625$.

By following these steps, you ensure that you don鈥檛 miss any part of the calculation process. This methodical approach is especially useful in algebra, where skipping steps can lead to errors.

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91影视

Find the value of \(a^{2}+b^{2}\) for the given values of a and \(b\) $$ a=7, b=24 $$

Short Answer

Step by step solution

- Square the value of a

- Square the value of b

- Add the squared values

Key Concepts

Squaring Numbers

Addition of Squares

Step-by-Step Problem Solving

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