Q. 8.78 Simplify:聽27p3-48p3256y53-32n53... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.78 (page 791)

Simplify:
$\sqrt{27 p^{3}} - \sqrt{48 p^{3}}$
$\sqrt[3]{256 y^{5}} - \sqrt[3]{32 n^{5}}$

Short Answer

Expert verified

Part a. $- p \sqrt{3 p}$

Part b. $4 y \sqrt[3]{4 y^{2}} - 2 n \sqrt[3]{4 n^{2}}$

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} 路 \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \sqrt{27 p^{3}} - \sqrt{48 p^{3}} & = & \sqrt{9 p^{2} 路 3 p} - \sqrt{16 p^{2} 路 3 p} \\ = & \sqrt{9 p^{2}} 路 \sqrt{3 p} - \sqrt{16 p^{2}} 路 \sqrt{3 p} \\ = & 3 p \sqrt{3 p} - 4 p \sqrt{3 p} \end{array}$

On combing the like radicals we get

role="math" localid="1644815489891" $\begin{array}{rcl} 3 p \sqrt{3 p} - 4 p \sqrt{3 p} & = & (3 - 4) p \sqrt{3 p} \\ = & - p \sqrt{3 p} \end{array}$

Part (b) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} 路 \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \sqrt[3]{256 y^{5}} - \sqrt[3]{32 n^{5}} & = & \sqrt[3]{64 y^{3} 路 4 y^{2}} - \sqrt[3]{8 n^{3} 路 4 n^{2}} \\ = & \sqrt[3]{64 y^{3}} 路 \sqrt[3]{4 y^{2}} - \sqrt[3]{8 n^{3}} 路 \sqrt[3]{4 n^{2}} \\ = & 4 y \sqrt[3]{4 y^{2}} - 2 n \sqrt[3]{4 n^{2}} \end{array}$

The indices are the same but the radicals are different. So they are not like radicals. And hence they cannot be simplified further.

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify:
$\sqrt{27 p^{3}} - \sqrt{48 p^{3}}$
$\sqrt[3]{256 y^{5}} - \sqrt[3]{32 n^{5}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Logic and Functions

Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Simplify:27p3-48p3256y53-32n53

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Logic and Functions

Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Simplify:
$\sqrt{27 p^{3}} - \sqrt{48 p^{3}}$
$\sqrt[3]{256 y^{5}} - \sqrt[3]{32 n^{5}}$