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Chapter 8: Problem 94

Simplify. $$ 2-108---\sqrt{3} $$

Short Answer

Expert verified
The expression simplifies to \(-106 + \sqrt{3}\).

Step by step solution

01

Identify the Expression Components

The expression given is \(2 - 108 - - \sqrt{3}\). Notice that there are double negative signs (---) preceding \(\sqrt{3}\), which suggests simplification is possible.
02

Simplify Double Negatives

The double negative --- before \(\sqrt{3}\) simplifies to a positive. This means the expression \(- - \sqrt{3}\) becomes \(+ \sqrt{3}\). Thus, the expression simplifies to \(2 - 108 + \sqrt{3}\).
03

Combine the Numerical Terms

Now, simplify the numerical part by combining the constants. Calculate \(2 - 108\) which equals \(-106\).
04

Rewrite the Simplified Expression

After combining the numeric terms, rewrite the full expression. The simplified form is \(-106 + \sqrt{3}\).

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Key Concepts

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

Order of Operations
When simplifying mathematical expressions, using the correct order of operations ensures accuracy. This sequence is often remembered with the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • First, solve any operations inside parentheses or brackets.
  • Next, address any exponents or radicals.
  • Then, perform all multiplications and divisions as they appear from left to right.
  • Finally, complete any additions and subtractions from left to right.

In our given problem, the primary operations are subtraction, a radical, and addition. We approached the task by first handling the double negatives, which transform into additions, then proceeded to handle simple arithmetic operations.
Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. They can represent quantities or relationships and are foundational in algebra.
  • Components of an expression include numbers (constants), letters (variables), and operational signs (like +, -, *, /).
  • Understanding how to manipulate these components is key to solving algebraic problems.

In our problem, the expression involves constants and the square root of a number. Simplification involves combining like terms, applying arithmetic rules, and utilizing algebraic techniques, like transforming double negatives.
Negative Numbers
Negative numbers are an essential part of arithmetic, representing values less than zero. Understanding how to work with them is crucial, especially in algebra.
  • Negative signs can change the direction of an operation, such as turning subtraction into addition.
  • Two negative signs in succession turn into a positive, due to the rule: a negative of a negative is positive.

In the expression given, identifying the double negative --- before \(\sqrt{3}\) simplifies them to a positive, changing the operation from subtraction to addition. This subtle transformation emphasizes how critical a comprehensive grasp of negative numbers is in simplification tasks.

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Most popular questions from this chapter

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