Chapter 9: Q 9.175 (page 1112)

Simplify a) $\sqrt[3]{27}$ b) $\sqrt[4]{256}$ c)localid="1648797668522" $\sqrt[5]{243}$

Short Answer

Expert verified

Part (a) $\sqrt[3]{27} = 3$

Part (b) $\sqrt[4]{256} = 4$

Part (c) $\sqrt[5]{243} = 3$

Step by step solution

Part (a) Step 1 : Given Information

The given expression is $\sqrt[3]{27}$ .

Part (a) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{m}} = a^{m \times \frac{1}{m}}$

localid="1648658709017" $\sqrt[3]{27} = {(27)}^{\frac{1}{3}} = {(3^{3})}^{\frac{1}{3}} = 3^{3 \times \frac{1}{3}} = 3$

Hence, localid="1648806131207" $\sqrt[3]{27} = 3$ .

Part (b) Step 1: Given information

The given expression is $\sqrt[4]{256}$ .

Part (b) Step 2: Simplification

Simplify $\sqrt[4]{256}$ as shown.

localid="1648803925100" $\sqrt[4]{256} = {(256)}^{\frac{1}{4}} = {(4^{4})}^{\frac{1}{4}} = 4$

Hence, localid="1648806139312" $\sqrt[4]{256} = 4$

Part (c) Step 1: Given information

The given expression is $\sqrt[5]{243}$ .

Part (c) Step 2: Simplification

Simplify $\sqrt[5]{243}$ as shown.

localid="1648804322300" $\sqrt[5]{243} = {(243)}^{\frac{1}{5}} = {(3^{5})}^{\frac{1}{5}} = 3$

Hence, localid="1648806147359" $\sqrt[5]{243} = 3$

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Simplify a) $\sqrt[3]{27}$ b) $\sqrt[4]{256}$ c)localid="1648797668522" $\sqrt[5]{243}$

Short Answer

Step by step solution

Part (a) Step 1 : Given Information

Part (a) Step 2: Simplification

Part (b) Step 1: Given information

Part (b) Step 2: Simplification

Part (c) Step 1: Given information

Part (c) Step 2: Simplification

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Simplify a)273b)2564c)localid="1648797668522" 2435

Short Answer

Step by step solution

Part (a) Step 1 : Given Information

Part (a) Step 2: Simplification

Part (b) Step 1: Given information

Part (b) Step 2: Simplification

Part (c) Step 1: Given information

Part (c) Step 2: Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Mechanics Maths

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Simplify a) $\sqrt[3]{27}$ b) $\sqrt[4]{256}$ c)localid="1648797668522" $\sqrt[5]{243}$