Q. 8.85 Simplify:聽(6-37)(3+47)(x3-2)(x3... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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.

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

Now combine the like radicals to get the simplifid expression.

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

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91影视

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

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91影视

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

Geometry

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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