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Chapter 2: Problem 57

Simplify. \(4^{2}+5^{2}\)

Short Answer

Expert verified
41

Step by step solution

01

Calculate the square of 4

First, determine the square of 4. This means calculating what is 4 multiplied by itself. Calculate: \(4^2 = 4 \times 4 = 16\)
02

Calculate the square of 5

Next, calculate the square of 5. This means multiplying 5 by itself. Calculate: \(5^2 = 5 \times 5 = 25\)
03

Add the results

Finally, add the results from the previous two steps. Calculate: \(4^2 + 5^2 = 16 + 25\) \(16 + 25 = 41\)

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Key Concepts

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

exponents
Exponents are a way to express repeated multiplication of the same number. For example, when you see something like 4^2, this means 4 is multiplied by itself 2 times (4 * 4). We call '4' the base and '2' the exponent.
Here's how to simplify an exponent:
  • First, write down the base number.
  • Next, multiply the base by itself as many times as the exponent indicates.
  • In our example, 4^2 means 4*4, which equals 16.
Working with exponents often shows up in math problems, so understanding this concept is very helpful!
basic arithmetic
Basic arithmetic involves the simplest and most fundamental operations in math: addition, subtraction, multiplication, and division. In the context of our problem, we used multiplication and addition.
Multiplication is combining equal groups of numbers. For example, in 4 * 4:
  • This shows you have 4 groups of 4.
  • This approach is what underlies exponentiation (repeated multiplication).
Addition, as we see in the final step of our problem, is simply combining numbers together to find their total. To simplify:
  • Calculate each term individually.
  • Add those results together to get the final answer.
These operations are foundational skills in math!
addition
Addition is one of the most basic and important operations in math. It is the process of bringing two or more numbers together to make a new total.
Here鈥檚 how it was used in the exercise:
  • In Step 3, the results of 4^2 (which is 16) and 5^2 (which is 25) were added together.
  • So, we added 16 and 25 to get the final answer: 41.
A quick tip for addition is to align numbers by their rightmost digits and add column by column, carrying over if necessary. It's essential to master addition as it's used in more complex math operations too!

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Most popular questions from this chapter

In the following exercises, identify each number as prime or composite. $$ 121 $$

In the following exercises, translate each English sentence into an algebraic equation and then solve it. List all the multiples of 4 that are less than 50 .

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