Chapter 8: Q. 8.40 (page 764)

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

Short Answer

Expert verified

Part a. After simplifying we get, $\frac{7}{9} .$

Part b. After simplifying we get, $\frac{2}{5} .$

Part c. After simplifying we get, $\frac{1}{3} .$

Step by step solution

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

So, $\sqrt{\frac{98}{162}} = \sqrt{\frac{49 \cdot 2}{81 \cdot 2}}$

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

Thus, $\sqrt{\frac{49 \cdot 2}{81 \cdot 2}} = \sqrt{\frac{49}{81}}$

Part a Step 3. Simplify

After simplifying we get,

$\sqrt{\frac{49}{81}} = \sqrt{\frac{{(7)}^{2}}{{(9)}^{2}}} = \frac{7}{9}$

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

So, $\sqrt[3]{\frac{24}{375}} = \sqrt[3]{\frac{8 \cdot 3}{125 \cdot 3}}$

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

Thus, $\sqrt[3]{\frac{8 \cdot 3}{125 \cdot 3}} = \sqrt[3]{\frac{8}{125}}$

Part b Step 3. Simplify

After simplifying we get,

$\sqrt[3]{\frac{8}{125}} = \sqrt[3]{\frac{{(2)}^{3}}{{(5)}^{3}}} = \frac{2}{5}$

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

So, $\sqrt[4]{\frac{4}{324}} = \sqrt[4]{\frac{1 \cdot 4}{81 \cdot 4}}$

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

Thus, $\sqrt[4]{\frac{1 \cdot 4}{81 \cdot 4}} \sqrt[4]{\frac{1}{81}}$

Part c Step 3. Simplify

After simplifying we get,

$\sqrt[4]{\frac{1}{81}} = \sqrt[4]{\frac{{(1)}^{4}}{{(3)}^{4}}} = \frac{1}{3}$

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

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:a98162b243753c43244

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

Logic and Functions

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Study anywhere. Anytime. Across all devices.

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