/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 Simplify. $$ 27--\sqrt{3} ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 21

Simplify. $$ 27--\sqrt{3} $$

Short Answer

Expert verified
The simplified form is \(27 + \sqrt{3}\).

Step by step solution

01

Simplify the Double Negative

The expression given is \(27--\sqrt{3}\). In mathematics, a double negative translates to a positive. That means when you have the subtraction of a negative number, it becomes addition. So, \(27--\sqrt{3}\) simplifies to \(27 + \sqrt{3}\).
02

Express the Simplified Form

After simplifying the double negative, the expression \(27 + \sqrt{3}\) is already in its simplest form since both 27 and \(\sqrt{3}\) are in their simplest expressions for the addition operation.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Double Negative
In algebra, understanding the concept of a double negative is crucial. When you encounter a double negative in a mathematical expression, it operates just like in regular language鈥攊t cancels out to become a positive. This is particularly common in subtraction problems. For example, if you see an expression like \(27 - -\sqrt{3}\), the double negative (\(- -\)) indicates that you actually add the two terms instead of subtracting them.
  • A double negative appears when you subtract a negative number.
  • Instead of "take away" a negative, you "add" the number.
  • This rule applies universally in mathematics.
This method of dealing with double negatives is essential as it forms the basis for further algebraic manipulations and simplifications.
Simplification
Simplification in mathematics involves reducing expressions to their simplest form. This means performing all possible arithmetic or algebraic operations until you can't reduce it further. With the example \(27 + \sqrt{3}\), simplification has already been achieved, as both terms are in their simplest form.
  • You simplify by combining like terms where possible.
  • Always perform operations, like resolving double negatives, first.
  • A simplified expression has no redundant operations or terms.
Understanding simplification helps to make mathematical problems more digestible and easier to work with, especially as you progress to more complex equations.
Mathematical Expressions
Mathematical expressions represent quantities and the relationships between them. They can include numbers, variables, and arithmetic operations. It's vital to structure them correctly for successful manipulation or simplification. The expression \(27 + \sqrt{3}\) is a basic form, involving a whole number and a square root.
  • Expressions consist of terms and operations (e.g., \(+, -, \times, \div\)).
  • They can represent real-world scenarios and abstract mathematical concepts.
  • Correctly aligning terms (positive or negative) is key to solving expressions.
Mastering expressions is essential in algebra, as they are the building blocks of more complex algebraic equations and functions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The time, \(t\), in seconds that an object is in free fall is given by the formula \(t=s \sqrt{4}\) where s represents the distance it has fallen in feet. Calculate the time it takes an object to fall, given the following distances. Give the exact value and the approximate value rounded off to the nearest tenth of a second. $$ 80 \text { feet } $$

Explain in your own words how to rationalize the denominator.

Explain why there are two square roots for any nonzero real number.

Rationalize the denominator $$ 14 x-\sqrt{3} $$

Rewrite the following as a radical expression with coefficient \(1 .\) $$ 52 x--\sqrt{3} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.