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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 8: Q14. (page 288)

Simplify
$\frac{3}{4} \sqrt{\frac{28}{3}}$

Short Answer

Expert verified

The final answer is $\frac{3}{4} \sqrt{\frac{28}{3}} = \frac{3}{2} \sqrt{\frac{7}{3}} .$

Step by step solution

01

Step 1. Given information:

The given expression is $\frac{3}{4} \sqrt{\frac{28}{3}}$ .

02

Step 2. Concept use.

Separate the factors into their own square roots.

Dividing by its denominator.

03

Step 3. Applying the concept.

Write the factors of given fractions separately.

$\frac{3}{4} \sqrt{\frac{28}{3}} = \frac{3}{4} \sqrt{\frac{2^{2} 脳 7}{3}}$

$= \frac{3}{4} 脳 2 \sqrt{\frac{7}{3}}$

$= 卤 \frac{3}{2} \sqrt{\frac{7}{3}}$

Since square root is positive quantity so we neglect negative sign.

Therefore, the simplified form is $\frac{3}{4} \sqrt{\frac{28}{3}} = \frac{3}{2} \sqrt{\frac{7}{3}} .$

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Most popular questions from this chapter

A rectangle has diagonal $2$ and length $\sqrt{3}$ . Find its width.

Use the diagram to complete each statement.

If $鈻� R S T ~ 鈻� ? ~ 鈻� ?$

Given: $P Q R S$ is a rectangle.

$P S$ is the geometric mean between $S T$ and $T R$ .

Prove: $鈭� P T Q$ is a right angle.

State an equation you could use to find the value of $x$ . Then find the value of $x$ in simplest radical form.

Simplify

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