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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.74 (page 790)

Simplify
$4 \sqrt{3 y} - 7 \sqrt{3 y} + 2 \sqrt{3 y}$
$6 \sqrt[3]{7 m n} + \sqrt[3]{7 m n} - 4 \sqrt[3]{7 m n}$

Short Answer

Expert verified

Part a. $- \sqrt{3 y}$

Part b. $3 \sqrt[3]{7 m n}$

Step by step solution

01

Part (a) Step 1. Combine the like radicals

In the expression $4 \sqrt{3 y} - 7 \sqrt{3 y} + 2 \sqrt{3 y}$ , all the radicals are like and so we can combine them. On combining them we get

$\begin{array}{rcl} 4 \sqrt{3 y} - 7 \sqrt{3 y} + 2 \sqrt{3 y} & = & (4 - 7 + 2) \sqrt{3 y} \\ = & - \sqrt{3 y} \end{array}$

02

Part (b) Step 1. Combine the like radicals

In the expression $6 \sqrt[3]{7 m n} + \sqrt[3]{7 m n} - 4 \sqrt[3]{7 m n}$ , all the radicals are like and so we can combine them. On combining them we get

$\begin{array}{rcl} 6 \sqrt[3]{7 m n} + \sqrt[3]{7 m n} - 4 \sqrt[3]{7 m n} & = & (6 + 1 - 4) \sqrt[3]{7 m n} \\ = & 3 \sqrt[3]{7 m n} \end{array}$

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[4]{3125}$ , b. $\sqrt[3]{81}$

Simplify:

$(a) \sqrt{\frac{98}{162}} (b) \sqrt[3]{\frac{24}{375}} (c) \sqrt[4]{\frac{4}{324}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{450}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{80 s^{15}}, \sqrt[5]{96 a^{7}}, \sqrt[6]{128 b^{7}}$

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