/*! 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 176 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 176

In the following exercises, simplify. $$ 11 \sqrt{2 r s}-9 \sqrt{2 r s}+3 \sqrt{2 r s} $$

Short Answer

Expert verified
5 \sqrt{2rs}\

Step by step solution

01

Identify like terms

Notice that all the terms in the expression share the same square root component, \( \sqrt{2rs} \). Therefore, they are like terms and can be combined.
02

Combine coefficients

Add the coefficients of the like terms together: \(11 - 9 + 3\). This results in \(5\).
03

Simplify the expression

Multiply the combined coefficient by the common square root component: \(5 \sqrt{2rs}\).

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.

Combining Like Terms
In algebra, simplifying expressions often involves combining like terms. Like terms are terms that have the same variable part. In our example, each term includes the square root component \( \sqrt{2rs} \). Since they share this component, they can be combined into a single term.
For instance:
  • 11 \( \sqrt{2rs} \)
  • -9 \( \sqrt{2rs} \)
  • 3 \( \sqrt{2rs} \)
are all like terms.
Combining them involves adding or subtracting their coefficients, which are the numerical parts of the terms. This process simplifies the expression and makes it easier to work with.
Coefficients
A coefficient is the numerical part of any term in an algebraic expression or equation. In the expression from our example:
  • 11 \( \sqrt{2rs} \)
  • -9 \( \sqrt{2rs} \)
  • 3 \( \sqrt{2rs} \)
the coefficients are 11, -9, and 3 respectively. When simplifying the expression, sum up these coefficients:
\[ 11 + (-9) + 3 = 5 \]
Thus, the combined coefficient is 5. This result multiplies the common square root component, making the simplified expression 5 \( \sqrt{2rs} \).
Square Roots
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 \( \times \) 2 equals 4. In our example, we deal with the square roots \( \sqrt{2rs} \).
This expression signifies the square root of the product of 2, r, and s. Key properties of square roots include:
  • Non-negative values - they are always greater than or equal to zero.
  • \

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) \(\sqrt[4]{16 x^{8}}\) (b) \(\sqrt[6]{64 y^{12}}\)

(a) Simplify \(\sqrt{\frac{27}{3}}\) and explain all your steps. (b) Simplify \(\sqrt{\frac{27}{5}}\) and explain all your steps. (c) Why are the two methods of simplifying square roots different?

In the following exercises, simplify and rationalize the denominator. $$ \frac{8}{\sqrt{3}} $$

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

In the following exercises, simplify and rationalize the denominator. $$ \frac{10}{\sqrt{6}} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Statistics

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.