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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. 245 (page 812)

In the following exercise , simplify
$(i) \frac{\sqrt{128}}{\sqrt{72}} (i i) \frac{\sqrt[3]{128}}{\sqrt[3]{54}}$

Short Answer

Expert verified

Part (a) The solution is $\frac{4}{3}$ .

Part (b) The solution is $\frac{4}{3}$ .

Step by step solution

01

Step 1. Given information

The given equation are $(i) \frac{\sqrt{128}}{\sqrt{72}} (i i) \frac{\sqrt[3]{128}}{\sqrt[3]{54}}$

02

Step 2. Calculation Part(a)

$(i) \frac{\sqrt{128}}{\sqrt{72}} = \frac{\sqrt{128}}{\sqrt{72}} Write the expression = \sqrt{\frac{128}{72}} Rewrite using quotient property = \sqrt{\frac{16}{9}} = \frac{4}{3} Hnece the simplified value is \frac{4}{3}$

03

Step 3. Calculation Part(b)

$(i i) \frac{\sqrt[3]{128}}{\sqrt[3]{54}} = \frac{\sqrt[3]{128}}{\sqrt[3]{54}} Write the expression = \sqrt[3]{\frac{128}{54}} Rewrite using quotient property = \sqrt[3]{\frac{64}{27}} = \frac{4}{3} Hence the simplified value is \frac{4}{3} .$

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