Chapter 8: Q. 14 (page 755)

In the following exercises, simplify.
$(a) \sqrt[3]{125} (b) \sqrt[4]{1296} (c) \sqrt[5]{1024}$

Short Answer

Expert verified

Hence,

$\begin{array}{l} (a) \sqrt[3]{125} = 5 \\ (b) \sqrt[4]{1296} = 6 \\ (c) \sqrt[5]{1024} = 4 \end{array}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenexpressionsare \\ (a) \sqrt[3]{125} (b) \sqrt[4]{1296} (c) \sqrt[5]{1024} \\ Wehavetosimplifythegivenexpressions. \end{array}$

Step 2. Simplify the expression in part (a)

$\begin{array}{l} \Rightarrow \sqrt[3]{125} = \sqrt[3]{{(5)}^{3}} [∵ 5^{3} = 125] \\ = 5 \end{array}$

Step 3. Simplify the expression in part (b)

$\begin{array}{l} \Rightarrow \sqrt[4]{1296} = \sqrt[4]{{(6)}^{4}} [∵ 6^{4} = 1296] \\ = 6 \end{array}$

Step 4. Simplify the expression in part (c)

$\begin{array}{l} \Rightarrow \sqrt[5]{1024} = \sqrt[5]{{(4)}^{5}} [∵ 4^{5} = 1024] \\ = 4 \end{array}$

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In the following exercises, simplify.
$(a) \sqrt[3]{125} (b) \sqrt[4]{1296} (c) \sqrt[5]{1024}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression in part (a)

Step 3. Simplify the expression in part (b)

Step 4. Simplify the expression in part (c)

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In the following exercises, simplify.a1253b12964c10245

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression in part (a)

Step 3. Simplify the expression in part (b)

Step 4. Simplify the expression in part (c)

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$(a) \sqrt[3]{125} (b) \sqrt[4]{1296} (c) \sqrt[5]{1024}$