Chapter 8: Q. 99 (page 772)

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{98 r^{5}}{100}}$

Short Answer

Expert verified

The simplified form is $\frac{7 r^{2} \sqrt{2 r}}{10}$ .

Step by step solution

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{98 r^{5}}{100}}$ .

Step 2. Write the concept.

To determine simplified form of a radical expression following formula is used:

$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} a n d \frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$

if $\sqrt[n]{a} a n d \sqrt[n]{b}$ are real numbers, $b \neq 0$ for any integer

$n \geq 2$ .

Step 3. Calculation.

Simplifying the expression.

$\sqrt{\frac{98 r^{5}}{100}} = \sqrt{\frac{49 r^{4} . 2 r}{100}} = \frac{\sqrt{49 r^{4} . 2 r}}{\sqrt{100}} = \frac{\sqrt{{(7 r^{2})}^{2} .} \sqrt{2 r}}{10} = \frac{7 |r^{2}| \sqrt{2 r}}{10} = \frac{7 r^{2} \sqrt{2 r}}{10}$

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.

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{98 r^{5}}{100}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Pure Maths

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the Quotient Property to simplify square roots.98r5100

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Pure Maths

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{98 r^{5}}{100}}$