Chapter 9: Q 451. (page 1124)

Simplify:
(a) $\sqrt[3]{a^{3}}$
(b) $\sqrt[12]{b^{12}}$

Short Answer

Expert verified

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

(b) $\sqrt[12]{b^{12}} = b$

Step by step solution

Part (a) Step 1: Given Information

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

Part (a) Step 2: Simplification

Since $a^{3} = {(a)}^{3}$

There is an odd root. There is no need for an absolute sign.

$\sqrt[3]{a^{3}} = a$

Part (b) Step 1: Given Information

The given expression is $\sqrt[12]{b^{12}}$

Part (b) Step 2: Simplification

Since $b^{12} = {(b)}^{12}$

We want positive root.

$\sqrt[12]{b^{12}} = b$

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Simplify:
(a) $\sqrt[3]{a^{3}}$
(b) $\sqrt[12]{b^{12}}$

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

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Simplify:(a) a33(b)b1212

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

One App. One Place for Learning.

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Simplify:
(a) $\sqrt[3]{a^{3}}$
(b) $\sqrt[12]{b^{12}}$