/*! 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 173 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 173

In the following exercises, simplify. $$ 5 \sqrt{3 a b}+\sqrt{3 a b}-2 \sqrt{3 a b} $$

Short Answer

Expert verified
The simplified form is \(4 \sqrt{3ab} \).

Step by step solution

01

- Identify Like Terms

In the expression given, identify the like terms. The terms are:\(5 \sqrt{3ab}\), \(\sqrt{3ab}\), and \(-2 \sqrt{3ab}\).
02

- Combine Like Terms

Combine the coefficients of the like terms. The combination is:\(5 \sqrt{3ab} + 1 \sqrt{3ab} - 2 \sqrt{3ab}\).
03

- Simplify the Coefficients

Add and subtract the coefficients:\(5 + 1 - 2 = 4\).So, the simplified form is:\(4 \sqrt{3ab}\).

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.

like terms
Like terms are terms that contain the same variables raised to the same power. In algebra, recognizing like terms is crucial.
This ensures that we only combine terms that can legally be added or subtracted.
For example, in the expression given, the terms are:
  • \(5 \sqrt{3ab}\)
  • \(\sqrt{3ab}\)
  • \(-2 \sqrt{3ab}\)
All of these terms include the expression \(\sqrt{3ab}\). That makes them like terms and can be combined.
combining coefficients
Once you have identified the like terms, you combine their coefficients. Coefficients are simply the numbers in front of a term. For instance:
  • In \(5 \sqrt{3ab}\), the coefficient is 5.
  • In \(\sqrt{3ab}\), the coefficient is 1 (since a single term without a number always implies 1).
  • In \(-2 \sqrt{3ab}\), the coefficient is -2.
These coefficients can be added or subtracted from each other while keeping the square root term \(\sqrt{3ab}\) as it is. This results in:
\(5 + 1 - 2\).
Simplifying this, you get 4. Thus, combining the coefficients gives you the term \(4 \sqrt{3ab}\).
simplification steps
To simplify an algebraic expression effectively:
  • Step 1: Identify the like terms. This involves recognizing terms that have the same root expression or variable combination.
  • Step 2: Combine the coefficients. This means adding or subtracting the numerical parts of the like terms.
    In our example, you performed:\(5 + 1 - 2 = 4\).
  • Step 3: Write the simplified expression. After combining the coefficients, place this number in front of the common square root or variable term.
So, the simplified form for the given example is:\(4 \sqrt{3ab}\).Remember, simplifying expressions helps make solving equations easier and understanding relationships between terms clearer.

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

In the following exercises, simplify. (a) \(\sqrt[6]{r^{12}}\) (b) \(\sqrt[3]{s^{30}}\)

In the following exercises, simplify. (a) \(\quad(\sqrt{15 y})\left(\sqrt{5 y^{3}}\right)\) (b) \(\left(\sqrt{2 n^{2}}\right)\left(\sqrt{18 n^{3}}\right)\)

Explain the difference between like radicals and unlike radicals. Make sure your answer makes sense for radicals containing both numbers and variables.

Simplify. $$ \sqrt{98 m^{5}} $$

Simplify. $$ \sqrt{450} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.