/*! 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 68 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 68

Perform the indicated operations. Simplify the answer when possible. \(3 \sqrt{54}-2 \sqrt{24}-\sqrt{96}+4 \sqrt{63}\)

Short Answer

Expert verified
\(\sqrt{6} + 12 \sqrt{7}\)

Step by step solution

01

Simplify the Roots

Start by simplifying each root expression. \n The root \( \sqrt{54} \) can be written as \( \sqrt{9*6} \), simplifying to \(3 \sqrt{6}\). \n The root \( \sqrt{24} \) can be written as \( \sqrt{4*6} \), simplifying to \(2 \sqrt{6}\). \n The root \( \sqrt{96} \) can be written as \( \sqrt{16*6} \), simplifying to \(4 \sqrt{6}\). \n The root \( \sqrt{63} \) can be written as \( \sqrt{9*7} \), simplifying to \(3 \sqrt{7}\).
02

Perform the indicated operations

Now, perform the indicated operations, that is, add and subtract the simplified roots. \n The given expression will simplify as follows: \(3*3 \sqrt{6} - 2*2 \sqrt{6} - 4 \sqrt{6} + 4*3 \sqrt{7} = 9 \sqrt{6} - 4 \sqrt{6} - 4 \sqrt{6} + 12 \sqrt{7}\)
03

Combine Like Terms

Combine the like roots, that is, those roots that have the same number under the root: \(9 \sqrt{6} - 4 \sqrt{6} - 4 \sqrt{6} \rightarrow 1 \sqrt{6}\)\n The roots \( \sqrt{7} \) don't have any other like terms, so they remain as is. So, the expression simplifies to: \( \sqrt{6} + 12 \sqrt{7}\).

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!

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

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{5}\), when \(a_{1}=4, r=3\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sequence \(1,4,8,13,19,26, \ldots\) is an arithmetic sequence.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=-2, r=-3\).
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

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.