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Chapter 8: Problem 36

Simplify the squares and square roots. $$3^{2}$$

Short Answer

Expert verified
3^{2} = 9

Step by step solution

01

Understand the Exponentiation

Understand that the expression involves raising the number 3 to the power of 2. This means multiplying 3 by itself.
02

Multiply the Numbers

Calculate the product of 3 multiplied by 3, which is equivalent to \(3 \times 3 \).
03

Simplify the Expression

The multiplication of 3 by itself results in 9. Therefore, \(3^{2} = 9\).

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Key Concepts

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

Exponentiation
Exponentiation is a fundamental mathematical operation used frequently in algebra and beyond. It involves raising a number, known as the 'base', to the power of an exponent. The exponent tells you how many times to multiply the base by itself.
For instance, in the expression \(3^{2}\), 3 is the base, and 2 is the exponent. This means we multiply 3 by itself two times: \(3 \times 3\).
Understanding exponentiation helps to simplify expressions and solve various types of equations effectively.
Multiplication
Multiplication is one of the basic arithmetic operations, and it is essential for working with exponents. When dealing with exponentiation, multiplication plays a key role in simplifying the expression.
For example, in the expression \(3^{2}\), we interpret this as multiplying 3 by itself. That means we perform the multiplication: \(3 \times 3\).
Multiplying these numbers gives us the product, which is 9. This multiplication step is crucial in converting the exponential expression into a simpler numerical form.
Understanding Exponents
To fully grasp exponentiation, it's important to understand what exponents represent and how they function. An exponent indicates the number of times a base is used as a factor.
For example, in the expression \(3^{2}\), the exponent 2 indicates that the base 3 is multiplied by itself once. This is why we perform the calculation: \(3 \times 3\).
Exponents can be viewed as a shorthand for repeated multiplication, making them very useful in mathematics. They simplify notation and calculations where numbers are multiplied by themselves multiple times.
Simplifying Expressions
Simplifying expressions is an essential skill in mathematics. It involves reducing complex expressions to their simplest form. When dealing with exponents, simplifying often means performing the multiplication indicated by the exponent.
In the example \(3^{2}\), simplifying the expression involves calculating \(3 \times 3\) to get 9. Thus, the simplified form of \(3^{2}\) is 9.
Simplifying expressions makes them more accessible and easier to work with, especially for further calculations or solving equations.

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