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Chapter 2: Problem 60

Simplify. \((3+7)^{2}\)

Short Answer

Expert verified
100

Step by step solution

01

Identify the components inside the parentheses

Identify the numbers inside the parentheses. In this case, it is \(3 + 7\).
02

Perform the addition

Add the numbers inside the parentheses: \(3 + 7 = 10\).
03

Square the result

Square the result from Step 2: \(10^{2}\). Calculate the square of 10, which is \(10 \times 10 = 100\).

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Key Concepts

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

Addition
Addition is one of the basic operations of arithmetic. When adding two numbers, you're essentially combining their values to get a sum.
For instance, in the given exercise, you have to add 3 and 7. Adding these together results in 10.

Let's break it down further:
  • You have two numbers: 3 and 7
  • Using the addition operation, you combine these two numbers: 3 + 7
  • The result, or sum, is 10.
Addition is a foundational skill that you'll use in more advanced math topics, making it crucial to understand this basic concept well.
Parentheses
Parentheses are symbols used in mathematics to group parts of an expression that should be evaluated first. They play a critical role in determining the order of operations in any expression. In the given exercise, the parentheses are used to group the addition operation.
Here鈥檚 how parentheses affect the calculation:
  • The expression inside the parentheses is \(3 + 7\)
  • This means you must first perform the addition operation inside the parentheses before doing anything else.
The correct order of operations ensures you get accurate results. This method is part of the PEMDAS/BODMAS rules, where operations within parentheses are prioritized.
Squaring Numbers
Squaring a number means multiplying that number by itself. This is indicated by raising the number to the power of 2, written as \(^2\).
In our exercise, after performing the addition inside the parentheses (3 + 7 = 10), you then need to square the result.

Here's the detailed process:
  • After calculating \(3 + 7\), you get 10.
  • To square this result, you multiply 10 by itself: 10 \times 10\.
  • The final result is 100.
Squaring numbers is useful in many areas of math, including geometry and algebra. It's important to understand this concept and how squaring changes the value of a number significantly.

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Most popular questions from this chapter

In the following exercises, simplify, using the order of operations. $$ (1+4)^{2} $$

In the following exercises, solve each equation using the addition property of equality. $$ y-3=19 $$

In the following exercises, find the least common multiple of each pair of numbers. $$ 25,35 $$

In the following exercises, simplify, using the order of operations. $$ 1+6(3-1) $$

In the following exercises, solve each equation using the subtraction property of equality. $$ s+62=95 $$
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