Chapter 9: Q 9.179. (page 1114)

Simplify a) $\sqrt{b^{2}}$ b) $\sqrt[3]{w^{3}}$ c) $\sqrt[4]{m^{4}}$ d) $\sqrt[5]{q^{5}}$

Short Answer

Expert verified

Part (a) $\sqrt{b^{2}} = |b|$

Part (b) $\sqrt[3]{w^{3}} = w$

Part (c) localid="1649380097114" $\sqrt[4]{m^{4}} = |m|$

Part (d) $\sqrt[5]{q^{5}} = q$

Step by step solution

Part (a) Step 1 . Given Information

The given expression is $\sqrt{b^{2}}$ .

Part (a) Step 2. Simplification

Since ${(b)}^{2} = b^{2}$ and we want the positive root.

$|b|$

So,

$\sqrt{b^{2}} = |b|$

Part (b) Step 1. Given information

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

Part (b) Step 2. Simplification

Since ${(w)}^{3} = w^{3}$ .

It is an odd root so there is no need for an absolute value sign.

$w$

So,

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

Part (c) Step 1. Given information

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

Part (c) Step 2. Simplification

Since ${(m)}^{4} = m^{4}$ and we want the positive root.

$|m|$

So,

$\sqrt[4]{m^{4}} = |m|$

Part (d) Step 1 . Given Information

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

Part (d) Step 2. Simplification

Since ${(q)}^{5} = q^{5}$ .

It is an odd root so there is no need for an absolute value sign.

$q$

so,

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

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Simplify a) $\sqrt{b^{2}}$ b) $\sqrt[3]{w^{3}}$ c) $\sqrt[4]{m^{4}}$ d) $\sqrt[5]{q^{5}}$

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

Part (d) Step 1 . Given Information

Part (d) Step 2. Simplification

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Simplify a)b2b)w33c)m44d)q55

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

Part (d) Step 1 . Given Information

Part (d) Step 2. Simplification

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Simplify a) $\sqrt{b^{2}}$ b) $\sqrt[3]{w^{3}}$ c) $\sqrt[4]{m^{4}}$ d) $\sqrt[5]{q^{5}}$