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Chapter 9: Problem 8

Simplify. $$ \sqrt{484} $$

Short Answer

Expert verified
The simplified form of \( \sqrt{484} \) is 22.

Step by step solution

01

Identify the Expression

Recognize that the task is to simplify the given square root expression: \(\sqrt{484}\).
02

Establish the Square Root

Find a number which, when multiplied by itself, gives 484. This number is referred to as the square root.
03

Calculate the Square Root

Calculate the square root of 484. Knowing that \(22 \times 22 = 484\), we find that \( \sqrt{484} = 22 \).

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Key Concepts

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

square root
A square root is a number that, when multiplied by itself, results in another number. For example, the square root of 9 is 3 because \text{3 x 3 = 9}. More formally, if \( x \) is a number and \( x^2 = n \), then \( x \) is the square root of \( n \). The square root symbol is \( \sqrt{} \).

For example, \( \sqrt{16} = 4 \), since \( 4 \times 4 = 16 \). The process of calculating square roots often involves identifying the number that produces a given value when squared.
simplification process
Simplifying expressions makes them easier to understand and work with. The goal is to find the simplest form of a mathematical expression. When simplifying square roots, it involves finding the principal (most basic) square root of a number. This involves:
  • Identifying the expression to simplify.
  • Finding pairs of identical factors inside the square root.
  • Reducing these pairs to simplify the expression further.

For instance, simplifying \( \sqrt{484} \) involves recognizing that this is a square root expression, finding the number that when squared equals 484, and simplifying down to this principal root.
mathematical expression
A mathematical expression is a combination of numbers, symbols, and operators (like +, -, *, /). They can represent a single value or a complex relationship between different values. Expressions involving square roots show the relationship between a number and its root.

For example, in the expression \( \sqrt{484} \), the radical symbol \( \sqrt{} \) indicates the square root of 484. Simplified, this evaluates to 22, as noted in steps in solving our given example.
basic arithmetic
Basic arithmetic involves simple operations like addition, subtraction, multiplication, and division. These operations form the foundation for more advanced mathematical concepts and processes.
Understanding basic arithmetic is crucial when working with square roots. For instance, knowing multiplication allows you to understand why \( 22 \times 22 = 484 \), which helps in identifying that \( \sqrt{484} = 22 \).
Therefore, a strong grasp of basic arithmetic helps you in simplifying more complex expressions.

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