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Chapter 9: Problem 71

Evaluate. \(1^{2}+2^{2}\)

Short Answer

Expert verified
5

Step by step solution

01

Evaluate the Square of 1

The problem requires calculating the square of 1. The square of a number is the product of the number by itself.\(1^2 = 1 \times 1 = 1\)
02

Evaluate the Square of 2

Next, calculate the square of 2 in the expression. Similar to before, multiply the number by itself.\(2^2 = 2 \times 2 = 4\)
03

Add the Squares Together

Finally, add the results from the previous steps together. This combines the evaluated squared terms.\(1 + 4 = 5\)

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Key Concepts

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

Understanding Squares
Calculating squares is a fundamental mathematical operation that you'll encounter frequently. When you square a number, you multiply the number by itself. For example, the square of 3, written as \(3^2\), is found by multiplying 3 by 3. This results in 9. Generally, \(n^2 = n \times n\), where \(n\) is the number you want to square.

Understanding how to square numbers simplifies many other mathematical operations. It is especially important when dealing with powers and polynomials. Here are some key points to remember about squares:
  • The square of a positive number is positive.
  • The square of zero is zero.
  • Negative numbers become positive when squared (e.g., \((-2)^2 = 4\)).
Exploring Addition
Addition is one of the four basic arithmetic operations, alongside subtraction, multiplication, and division. It involves finding the total or sum by combining two or more numbers.

In the exercise, after finding each square, the next step is to add them together. When you add numbers, it doesn't matter what order you add them in鈥攖his is called the commutative property of addition. For example, \(1 + 2 = 2 + 1\).

Some tips for performing successful addition include:
  • Stack numbers vertically if adding many numbers, aligning them by their rightmost digits.
  • Double-check your work by reversing the order to verify the sum.
  • If using mental math, group numbers into tens or easily manageable numbers first.
Step-by-Step Solution Simplified
Following a step-by-step solution can be essential for avoiding mistakes and fully understanding a mathematical concept. Breaking down a problem into smaller, manageable parts helps to focus on one task at a time.

The process for evaluating the expression \(1^2 + 2^2\) is a great example of this:
  • First, find the square of each number individually: start with \(1^2\), which equals 1, and then \(2^2\), which equals 4.
  • Once you have these results, you move on to the second part: addition. By adding these squares, \(1 + 4 = 5\), you find the final answer.
By practicing this approach, you'll gain better accuracy and confidence in solving similar mathematical problems that require multiple steps.

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Most popular questions from this chapter

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