/*! 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 44 Add or subtract terms whenever p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 44

Add or subtract terms whenever possible. $$3 \sqrt{54}-2 \sqrt{24}-\sqrt{96}+4 \sqrt{63}$$

Short Answer

Expert verified
The simplified form of the original expression is \(\sqrt{6} + 12\sqrt{7}\).

Step by step solution

01

Simplify each term

First, simplify each of the four terms individually. Do so by trying to express the number under the square root as a product of a perfect square and another integer. \n1. \(3 \sqrt{54}\) = 3 * \(\sqrt{9 * 6}\) = 3 * \(\sqrt{9}\) * \(\sqrt{6}\) = 3 * 3 * \(\sqrt{6}\) = \(9 \sqrt{6}\).\n2. \(2 \sqrt{24}\) = 2 * \(\sqrt{4 * 6}\) = 2 * \(\sqrt{4}\) * \(\sqrt{6}\) = 2 * 2 * \(\sqrt{6}\) = \(4 \sqrt{6}\).\n3. \(\sqrt{96}\) = \(\sqrt{16 * 6}\) = \(\sqrt{16}\) * \(\sqrt{6}\) = 4 * \(\sqrt{6}\).\n4. \(4 \sqrt{63}\) = 4 * \(\sqrt{9 * 7}\) = 4 * \(\sqrt{9}\) * \(\sqrt{7}\) = 4 * 3 * \(\sqrt{7}\) = \(12 \sqrt{7}\).
02

Rewrite original expression

Substitute the simplified terms into the original expression: \(9\sqrt{6} - 4\sqrt{6} - 4\sqrt{6} + 12\sqrt{7}\).
03

Combine like terms

Combine the terms that have the same radical part: \(9\sqrt{6} - 4\sqrt{6} - 4\sqrt{6} = 1\sqrt{6}\). So the final simplified expression is \(\sqrt{6} + 12\sqrt{7}\).

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

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$

In Exercises 136鈥�143, determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$4^{-2}<4^{-3}$$

Fill in each box to make the statement true. $$\sqrt{x}=5 x^{7}$$

Evaluate each exponential expression in $$\frac{x^{14}}{x^{-7}}$$

Simplify by reducing the index of the radical. $$\sqrt[4]{5^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.