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Chapter 3: Problem 28

\(5^{2}=\) ?

Short Answer

Expert verified
25

Step by step solution

01

Understand the Problem

The problem asks us to calculate the square of 5. Squaring a number means multiplying the number by itself. Hence, we need to calculate \(5 \times 5\).
02

Perform the Multiplication

Multiply 5 by itself to find its square: \(5 \times 5 = 25\).
03

State the Result

The result of squaring 5 is \(25\).

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Key Concepts

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

Multiplication
Multiplication is one of the fundamental arithmetic operations that involves combining equal groups. In the exercise, the number 5 is squared, which means it is multiplied by itself.
When we multiply 5 times 5, it is similar to adding 5 together five times.
This operation is often represented in mathematical expressions as the exponent "2", indicating that a number is used as a multiplier twice.
  • Example: The expression \(5^2\) signifies that 5 is multiplied by 5.
  • Result: Here, \(5 \times 5 = 25\).
Understanding multiplication helps in solving more complex equations and is essential for advanced mathematical concepts.
Number Operations
Number operations include addition, subtraction, multiplication, and division. Each operation serves a unique function in mathematics.
For squaring numbers, multiplication is used again. This operation simplifies repetitive addition and offers a concise way to express larger quantities.
Number operations are applicable in various everyday situations:
  • Sharing groceries among people (division).
  • Accumulating scores in games (addition).
  • Adjusting areas of squares (multiplication).
In the exercise provided, knowing how to effectively perform these operations ensures that problems are resolved accurately and efficiently.
Mathematical Concepts
Mathematics encompasses a wide range of concepts such as exponents, fractions, and squares. These concepts are built on basic arithmetic operations, including multiplication.
Understanding mathematical concepts like exponents allows us to express operations in a more compact form.
The exercise of calculating \(5^2\) introduces the concept of exponents, where a number, known as the base, is multiplied by itself as indicated by the exponent value.
  • Exponentiation: It simplifies complex multiplications and helps conceal repeated operations.
  • Squared numbers: A specific type of exponentiation where the exponent is 2.
Mastery of these foundational concepts is critical for progressing to topics like algebra and calculus. They build the groundwork for advanced mathematical thinking and problem-solving.

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Most popular questions from this chapter

\(\frac{1}{2} \cdot \frac{2}{3}=\) ?

\((10)(3) \div 2=\) ?

\(\frac{6}{3}=\) ?

Use addition and/or subtraction to solve these equations: a. \(5+x=3-7\) b. \(x-3=10\) c. \(x-3+2=8 \div 4\)

\((-3)(-4)=\) ?
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