Chapter 8: Q. 8.56 (page 777)

Simplify::
(a) $100^{\frac{1}{2}}$
(b) $27^{\frac{1}{3}}$
(c) $81^{\frac{1}{4}}$

Short Answer

Expert verified

The simplification of $100^{\frac{1}{2}}$ is $10$

The simplification of $27^{\frac{1}{3}}$ is $3$

The simplification of $81^{\frac{1}{4}}$ is $3$

Step by step solution

Part (a) Step 1. Given

An expression $100^{\frac{1}{2}}$

To simplify the expression.

Part (a) Step 2. Rewrite as perfect nth power

Rewrite as a square root.

$100^{\frac{1}{2}} = \sqrt{100}$

Recognize $100$ as a perfect square.

$= \sqrt{10^{2}}$

$= 10$

Part (b) Step 1. Given

An expression $27^{\frac{1}{3}}$

To simplify the expression.

Part (b) Step 2. Rewrite as perfect nth power

Rewrite as a cube root.

$27^{\frac{1}{3}} = \sqrt[3]{27}$

Recognize $27$ as a perfect cube.

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

$= 3$

Part (c) Step 1. Given

An expression $81^{\frac{1}{4}}$

To simplify the expression.

Part (c) Step 2. Rewrite as perfect nth power

Rewrite as a fourth root.

$81^{\frac{1}{4}} = \sqrt[4]{81}$

Recognize $81$ as a perfect fourth power.

$= \sqrt[4]{3^{4}}$

$= 3$

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Simplify::
(a) $100^{\frac{1}{2}}$
(b) $27^{\frac{1}{3}}$
(c) $81^{\frac{1}{4}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite as perfect nth power

Part (b) Step 1. Given

Part (b) Step 2. Rewrite as perfect nth power

Part (c) Step 1. Given

Part (c) Step 2. Rewrite as perfect nth power

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Simplify::(a)10012(b)2713(c) 8114

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite as perfect nth power

Part (b) Step 1. Given

Part (b) Step 2. Rewrite as perfect nth power

Part (c) Step 1. Given

Part (c) Step 2. Rewrite as perfect nth power

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Applied Mathematics

Geometry

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Simplify::
(a) $100^{\frac{1}{2}}$
(b) $27^{\frac{1}{3}}$
(c) $81^{\frac{1}{4}}$