Problem 93 Simplify. $$ 5-48---\sqrt{3}... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 8: Problem 93

Simplify. $$ 5-48---\sqrt{3} $$

Short Answer

Expert verified

The simplified expression is \$-43 + \\sqrt{3}\$.

Step by step solution

Simplify Consecutive Minus Signs

When you have consecutive minus signs, such as $---$, it simplifies to a plus sign. Therefore, $5 - 48 --- \sqrt{3} = 5 - 48 + \sqrt{3}$. This is because two minus signs \"cancel\" each other out, and the third one changes sign back to negative.

Perform the Basic Arithmetic

With the expression $5 - 48 + \sqrt{3}$, calculate $5 - 48$ first, which equals $-43$. Thus, the expression becomes $-43 + \sqrt{3}$.

Combine the Terms

Since $-43$ is a constant number and $\sqrt{3}$ is an irrational number, they cannot combine further. Hence, the simplified form of the expression is $-43 + \sqrt{3}$.

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Key Concepts

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

Consecutive Signs

In mathematics, managing signs efficiently is crucial for simplifying expressions. When you see consecutive signs, like a series of minus signs, remember that they can often be simplified. Consider a situation where you encounter three minus signs in a row, such as in the expression $5 - 48 --- \sqrt{3}$. These consecutive minus signs may initially appear confusing, but they follow a basic rule: two minus signs cancel each other out to become a plus sign. Therefore, $---$ simplifies to $+$, and the expression becomes $5 - 48 + \sqrt{3}$. Understanding this rule can significantly ease the process of simplifying mathematical expressions.

Basic Arithmetic

Basic arithmetic involves the foundational operations of addition, subtraction, multiplication, and division. These operations are essential tools for simplifying expressions. When simplifying an expression like $5 - 48 + \sqrt{3}$, it's important to perform operations sequentially. Start with solving the operations between regular numbers. For instance:

Begin with $5 - 48$.
This subtracts 48 from 5, resulting in $-43$.

The expression is thereby reduced to $-43 + \sqrt{3}$. Basic arithmetic ensures that we properly compute each part of an expression before moving on.

Irrational Numbers

Irrational numbers are numbers that cannot be expressed as simple fractions. They have decimal expansions that are non-repeating and non-terminating. Examples of irrational numbers include $\sqrt{2}, \sqrt{3},$ and $\pi$. In the expression $-43 + \sqrt{3}$, $\sqrt{3}$ is an irrational number. You cannot combine integers and irrational numbers directly as terms, because they do not share the same nature:

$-43$ is an integer, a complete whole number.
$\sqrt{3}$ is irrational, with no exact fractional representation.

Thus, the expression $-43 + \sqrt{3}$ remains in its simplified form, with each part representing different properties in mathematics.

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91影视

Simplify. $$ 5-48---\sqrt{3} $$

Short Answer

Step by step solution

Simplify Consecutive Minus Signs

Perform the Basic Arithmetic

Combine the Terms

Key Concepts

Consecutive Signs

Basic Arithmetic

Irrational Numbers

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