Chapter 8: Q 137E (page 786)

In the following exercises, simplify.
Part (a): ${(- 36)}^{\frac{1}{2}}$
Part (b): $- 36^{\frac{1}{2}}$
Part (c): ${(36)}^{\frac{- 1}{2}}$

Short Answer

Expert verified

Part (a): On simplifying, we know the solution is not real.

Part (b): On simplifying, we get $- 6$ .

Part (c): On simplifying, we get role="math" localid="1644772580964" $\frac{1}{6}$ .

Step by step solution

Part (a) Step 1. Rewrite as a root.

Consider the given question,

${(- 36)}^{\frac{1}{2}}$

Rewrite as a square root,

$= \sqrt[2]{{(- 36)}^{2}}$

The solution is not real.

Part (b) Step 1. Rewrite as a root.

Consider the given question,

$- 36^{\frac{1}{2}}$

The exponent only applies to the $36$ .

Rewrite as a square root,

$= - \sqrt[2]{36}$

On simplifying the expression,

$= - \sqrt[2]{6^{2}} = - 6$

Part (c) Step 1. Rewrite as a root.

Consider the given question,

${(36)}^{\frac{- 1}{2}}$

Rewrite using the property $a^{- n} = \frac{1}{a^{n}}$ ,

$= \frac{1}{{(36)}^{\frac{1}{2}}}$

Rewrite as a square root,

$= \frac{1}{\sqrt[2]{36}}$

On simplifying the expression,

$= \frac{1}{\sqrt[2]{6^{2}}} = \frac{1}{6}$

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In the following exercises, simplify.
Part (a): ${(- 36)}^{\frac{1}{2}}$
Part (b): $- 36^{\frac{1}{2}}$
Part (c): ${(36)}^{\frac{- 1}{2}}$

Short Answer

Step by step solution

Part (a) Step 1. Rewrite as a root.

Part (b) Step 1. Rewrite as a root.

Part (c) Step 1. Rewrite as a root.

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In the following exercises, simplify.Part (a):-3612Part (b): -3612Part (c):36-12

Short Answer

Step by step solution

Part (a) Step 1. Rewrite as a root.

Part (b) Step 1. Rewrite as a root.

Part (c) Step 1. Rewrite as a root.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Mechanics Maths

Decision Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
Part (a): ${(- 36)}^{\frac{1}{2}}$
Part (b): $- 36^{\frac{1}{2}}$
Part (c): ${(36)}^{\frac{- 1}{2}}$