/*! 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 46 Simplify. $$ 100,000--\sqrt{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 46

Simplify. $$ 100,000--\sqrt{5} $$

Short Answer

Expert verified
The simplified form is \( 100,000 + \sqrt{5} \).

Step by step solution

01

Identify the Mathematical Operation

Examine the expression \( 100,000 - (-\sqrt{5}) \). Notice the subtraction sign and the negative square root of 5. In mathematics, subtracting a negative number is the same as adding the positive version of that number.
02

Apply the Rule for Double Negatives

According to mathematical rules, subtracting a negative number involves turning it into an addition. Thus, \( 100,000 - (-\sqrt{5}) \) becomes \( 100,000 + \sqrt{5} \).
03

Write the Final Simplified Expression

Now write out the final expression: \( 100,000 + \sqrt{5} \). This is the simplified form of the original expression since there are no further operations or like terms to combine.

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.

Understanding Double Negatives in Mathematics
The concept of double negatives can seem tricky at first, but it actually simplifies expressions in mathematics. When you encounter a negative sign followed by another negative sign, it's a situation we call a "double negative."

But what does it mean exactly? Simply put, when you subtract a negative number, it becomes an addition. This is because the two negatives cancel each other out, transforming the operation from subtraction to addition in mathematical terms.
  • For instance, in the expression \( 100,000 - (-\sqrt{5}) \), we see a `-(-)` situation.
  • Here, the double negative translates to \( 100,000 + \sqrt{5} \).
This is a fundamental property of numbers that always holds true: wherever you find two negatives together, you add instead.
Grasping the Concept of Square Roots
The square root is another crucial mathematical operation, which helps in simplifying numbers. A square root answers the question: "What number, when multiplied by itself, gives me this original number?"

For example, the square root of 25 is 5 because \( 5 \times 5 = 25 \). In mathematical terms, we denote the square root by the radical symbol \( \sqrt{} \).
  • In our expression, we're looking at \( \sqrt{5} \), which indicates a number that when squared equals 5.
  • Though \( \sqrt{5} \) does not yield a neat whole number, it is essential in maintaining the expression's structure when simplifying.
Simplifying expressions with square roots sometimes allows us to approximate values or retain them as irrational numbers.
Mastering Mathematical Operations
Mathematical operations are the building blocks of algebra and arithmetic, and learning how they interact is vital for solving equations. The primary operations include addition, subtraction, multiplication, and division.

In simplification exercises like ours, it's important to correctly apply these operations to derive a more concise expression.
  • Start by identifying each operation: Look at \( 100,000 - (-\sqrt{5}) \), spotting the subtraction and double negative.
  • Apply what you know about these operations: Here, convert the subtraction of a negative into an addition.
Mastering these basic principles makes it much simpler to tackle complex expressions, enabling clear and correct simplification.

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

Simplify. \(4162--\sqrt{3}-2384--\sqrt{3}-3750---\sqrt{3}\)

Simplify. (Assume all radicands containing variable expressions are positive.) \(12 m 4 n--n-m 75 m 2 n--n--v+227 m 4 n-\ldots-n-V\)

Simplify. (Assume all radicands containing variable expressions are positive.) \(a \cdot 3 b--\sqrt{5}+4 a \cdot 3 b--\sqrt{5}-a \cdot 3 b-\sqrt{5}\)

Simplify. (Assume all radicands containing variable expressions are positive.) \(125 x y 3------\sqrt{3}+8 x 3 y---\sqrt{3}-216 x y 3------\sqrt{3}+10 x \cdot y \sqrt{3}\)

Write as a radical and then simplify. $$(14) 3 / 2$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.