Chapter 8: Q. 8.39 (page 764)

Simplify:
$(a) \sqrt{\frac{75}{48}} (b) \sqrt[3]{\frac{54}{250}} (c) \sqrt[4]{\frac{32}{162}}$

Short Answer

Expert verified

Part a. After simplifying we get, $\frac{5}{4} .$

Part b. After simplifying we get, $\frac{3}{5} .$

Part c. After simplifying we get, $\frac{2}{3} .$

Step by step solution

Part a Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Thus, $\sqrt{\frac{75}{48}} = \sqrt{\frac{25 \cdot 3}{16 \cdot 3}}$

Part a Step 2. Simplify the fraction by removing common factors

So, $\sqrt{\frac{25 \cdot 3}{16 \cdot 3}} = \sqrt{\frac{25}{16}}$

Part a Step 3. Simplify

After simplifying we get,

$\sqrt{\frac{25}{16}} = \sqrt{\frac{{(5)}^{2}}{{(4)}^{2}}} = \frac{5}{4}$

Part b Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Thus, $\sqrt[3]{\frac{54}{250}} = \sqrt[3]{\frac{27 \cdot 2}{125 \cdot 2}}$

Part b Step 2. Simplify the fraction by removing common factors

So, $\sqrt[3]{\frac{27 \cdot 2}{125 \cdot 2}} = \sqrt[3]{\frac{27}{125}}$

Part b Step 3. Simplify

After simplifying we get,

$\sqrt[3]{\frac{27}{125}} = \sqrt[3]{\frac{{(3)}^{3}}{{(5)}^{3}}} = \frac{3}{5}$

Part c Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Thus, $\sqrt[4]{\frac{32}{162}} = \sqrt[4]{\frac{16 \cdot 2}{81 \cdot 2}}$

Part c Step 2. Simplify the fraction by removing common factors

So, $\sqrt[4]{\frac{16 \cdot 2}{81 \cdot 2}} \sqrt[4]{\frac{16}{81}}$

Part c Step 3. Simplify

After simplifying we get,

$\sqrt[4]{\frac{16}{81}} = \sqrt[4]{\frac{{(2)}^{4}}{{(3)}^{4}}} = \frac{2}{3}$

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Simplify:
$(a) \sqrt{\frac{75}{48}} (b) \sqrt[3]{\frac{54}{250}} (c) \sqrt[4]{\frac{32}{162}}$

Short Answer

Step by step solution

Part a Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Part a Step 2. Simplify the fraction by removing common factors

Part a Step 3. Simplify

Part b Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Part b Step 2. Simplify the fraction by removing common factors

Part b Step 3. Simplify

Part c Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Part c Step 2. Simplify the fraction by removing common factors

Part c Step 3. Simplify

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Simplify:a7548b542503c321624

Short Answer

Step by step solution

Part a Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Part a Step 2. Simplify the fraction by removing common factors

Part a Step 3. Simplify

Part b Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Part b Step 2. Simplify the fraction by removing common factors

Part b Step 3. Simplify

Part c Step 1. Rewrite the radicand as a product using the largest perfect square factor inside the radical

Part c Step 2. Simplify the fraction by removing common factors

Part c Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \sqrt{\frac{75}{48}} (b) \sqrt[3]{\frac{54}{250}} (c) \sqrt[4]{\frac{32}{162}}$