Chapter 8: Q 8.77TI (page 791)

Simplify:
$\sqrt{32 m^{7}} - \sqrt{50 m^{7}}$
$\sqrt[3]{135 x^{7}} - \sqrt[3]{40 x^{7}}$

Short Answer

Expert verified

Part a. $- m^{3} \sqrt{2 m}$

Part b. localid="1645681976813" $x^{2} \sqrt[3]{5 x}$

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \sqrt{32 m^{7}} - \sqrt{50 m^{7}} & = & \sqrt{16 m^{6} \cdot 2 m} - \sqrt{25 m^{6} \cdot 2 m} \\ = & \sqrt{16 m^{6}} \cdot \sqrt{2 m} - \sqrt{25 m^{6}} \cdot \sqrt{2 m} \\ = & 4 m^{3} \sqrt{2 m} - 5 m^{3} \sqrt{2 m} \end{array}$

On combing the like radicals we get

$\begin{array}{rcl} 4 m^{3} \sqrt{2 m} - 5 m^{3} \sqrt{2 m} & = & (4 - 5) m^{3} \sqrt{2 m} \\ = & - m^{3} \sqrt{2 m} \end{array}$

Part (b) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ simplify the expression.

localid="1645681992780" $\begin{array}{rcl} \sqrt[3]{135 x^{7}} - \sqrt[3]{40 x^{7}} & = & \sqrt[3]{27 x^{6} \cdot 5 x} - \sqrt[3]{8 x^{6} \cdot 5 x} \\ = & \sqrt[3]{27 x^{6}} \cdot \sqrt[3]{5 x} - \sqrt[3]{8 x^{6}} \cdot \sqrt[3]{5 x} \\ = & 3 x^{2} \cdot \sqrt[3]{5 x} - 2 x^{2} \cdot \sqrt[3]{5 x} \end{array}$

On combing the like radicals we get

localid="1645682007270" $3 x^{2} \cdot \sqrt[3]{5 x} - 2 x^{2} \cdot \sqrt[3]{5 x} = (3 - 2) x^{2} \sqrt[3]{5 x} = x^{2} \sqrt[3]{5 x}$

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Simplify:
$\sqrt{32 m^{7}} - \sqrt{50 m^{7}}$
$\sqrt[3]{135 x^{7}} - \sqrt[3]{40 x^{7}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

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Simplify:32m7-50m7135x73-40x73

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Calculus

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify:
$\sqrt{32 m^{7}} - \sqrt{50 m^{7}}$
$\sqrt[3]{135 x^{7}} - \sqrt[3]{40 x^{7}}$