Chapter 9: Q 100. (page 1053)

In the following exercises, simplify.
$\frac{15 + \sqrt{75}}{5}$

Short Answer

Expert verified

The required answer is $(3 + \sqrt{3})$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{15 + \sqrt{75}}{5}$

Step 2. Use the Product Property to Simplify Square Root.

$\frac{15 + \sqrt{75}}{5}$

Rewrite the radicand as a product using the largest perfect square factor.

$\frac{15 + \sqrt{25 \cdot 3}}{5}$

Rewrite the radical as the product of two radicals.

$\frac{15 + \sqrt{25} \cdot \sqrt{3}}{5}$

Simplify,

$\frac{15 + 5 \sqrt{3}}{5}$

Factor the common factor from the numerator,

$\frac{5 (3 + \sqrt{3})}{5}$

Remove the common factor and simplify,

$(3 + \sqrt{3})$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, simplify.
$\frac{15 + \sqrt{75}}{5}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the Product Property to Simplify Square Root.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Mechanics Maths

Logic and Functions

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.15+755

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the Product Property to Simplify Square Root.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Mechanics Maths

Logic and Functions

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\frac{15 + \sqrt{75}}{5}$