/*! 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 72 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 72

Perform the indicated operations. Simplify the answer when possible. \(\frac{\sqrt{27}}{2}+\frac{\sqrt{75}}{7}\)

Short Answer

Expert verified
The simplified result of the expression \(\frac{\sqrt{27}}{2}+\frac{\sqrt{75}}{7}\) is \(\frac{31\sqrt{3}}{14}\).

Step by step solution

01

Simplify the square roots.

Start by simplifying the square roots. Firstly, \(\sqrt{27}\) can be written as \(\sqrt{3^3}\), which equals to 3\(\sqrt{3}\). Secondly, \(\sqrt{75}\) can be written as \(\sqrt{3*5^2}\), which equals to 5\(\sqrt{3}\).
02

Substitute the simplified square roots back into the fractions.

After simplifying the square roots, substitute the simplified square roots back into the fractions. We get \(\frac{3\sqrt{3}}{2}+\frac{5\sqrt{3}}{7}\).
03

Find a common denominator and perform the addition.

To perform the addition, find a common denominator. The least common denominator of 2 and 7 is 14. Rewrite the fractions with the common denominator: \(\frac{21\sqrt{3}}{14}+\frac{10\sqrt{3}}{14}\). Perform the addition to get the final result, which is \(\frac{31\sqrt{3}}{14}\).

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

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a sequence is geometric, we can write as many terms as we want by repeatedly multiplying by the common ratio.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,3, \frac{3}{2}, \frac{3}{4}, \ldots\)

What is a sequence? Give an example with your description.

What is a geometric sequence? Give an example with your description.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.