Chapter 11: Q. 8.85 (page 1069)

Simplify:
$(6 - 3 \sqrt{7}) (3 + 4 \sqrt{7})$
$(\sqrt[3]{x} - 2) (\sqrt[3]{x} - 3)$

Short Answer

Expert verified

Part a. $- 66 + 15 \sqrt{7}$

Part b. $\begin{array}{rcl} \sqrt[3]{x^{2}} - 5 \sqrt[3]{x} + 6 \end{array}$

Step by step solution

Part (a) Step 1. Expand the expression and simplify the radicals

Multiply and expand the expression.

$\begin{array}{rcl} (6 - 3 \sqrt{7}) (3 + 4 \sqrt{7}) & = & 18 + 24 \sqrt{7} - 9 \sqrt{7} - 12 {(\sqrt{7})}^{2} \\ = & 18 + 24 \sqrt{7} - 9 \sqrt{7} - 84 \end{array}$

Now combine the like numbers and like radicals to get the simplified answer.

$\begin{array}{rcl} 18 + 24 \sqrt{7} - 9 \sqrt{7} - 84 & = & (18 - 84) + (24 \sqrt{7} - 9 \sqrt{7}) \\ = & - 66 + (24 - 9) \sqrt{7} \\ = & - 66 + 15 \sqrt{7} \end{array}$

Part (b) Step 1. Expand the expression and simplify the radicals

Multiply and expand the expression.

$\begin{array}{rcl} (\sqrt[3]{x} - 2) (\sqrt[3]{x} - 3) & = & \sqrt[3]{x} \cdot \sqrt[3]{x} - 3 \sqrt[3]{x} - 2 \sqrt[3]{x} + 6 \\ = & \sqrt[3]{x^{2}} - 3 \sqrt[3]{x} - 2 \sqrt[3]{x} + 6 \end{array}$

Now combine the like radicals to get the simplifid expression.

$\begin{array}{rcl} \sqrt[3]{x^{2}} - 3 \sqrt[3]{x} - 2 \sqrt[3]{x} + 6 & = & \sqrt[3]{x^{2}} - (3 + 2) \sqrt[3]{x} + 6 \\ = & \sqrt[3]{x^{2}} - 5 \sqrt[3]{x} + 6 \end{array}$

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.

Simplify:
$(6 - 3 \sqrt{7}) (3 + 4 \sqrt{7})$
$(\sqrt[3]{x} - 2) (\sqrt[3]{x} - 3)$

Short Answer

Step by step solution

Part (a) Step 1. Expand the expression and simplify the radicals

Part (b) Step 1. Expand the expression and simplify the radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Discrete Mathematics

Geometry

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Simplify:(6-37)(3+47)(x3-2)(x3-3)

Short Answer

Step by step solution

Part (a) Step 1. Expand the expression and simplify the radicals

Part (b) Step 1. Expand the expression and simplify the radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Discrete Mathematics

Geometry

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Simplify:
$(6 - 3 \sqrt{7}) (3 + 4 \sqrt{7})$
$(\sqrt[3]{x} - 2) (\sqrt[3]{x} - 3)$