Chapter 9: Q 450. (page 1124)

Simplify:
(a) $\sqrt[5]{u^{5}}$
(b) $\sqrt[8]{v^{8}}$

Short Answer

Expert verified

(a) $\sqrt[5]{u^{5}} = u$

(b)localid="1650566886869" $\sqrt[8]{v^{8}} = |v|$

Step by step solution

Part (a) Step 1: Given Information

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

Part (a) Step 2: Simplification

Since ${(u)}^{5} = u^{5}$

There is an odd root. So there is no need for an absolute value sign.

$\sqrt[5]{u^{5}} = u$

Part (b) Step 1: Given Information

The given expression is $\sqrt[8]{v^{8}}$

Part (b) Step 2: Simplification

Since $v^{8} = {(v)}^{8}$

We want positive roots.

$\sqrt[8]{v^{8}} = |v|$

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Simplify:
(a) $\sqrt[5]{u^{5}}$
(b) $\sqrt[8]{v^{8}}$

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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Short Answer

Step by step solution

Part (a) Step 1: Given Information

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Simplify:
(a) $\sqrt[5]{u^{5}}$
(b) $\sqrt[8]{v^{8}}$