Q. 16 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 15–24, approximate each number using a calculator. Express your answer rounded to three decimal places.

(a) $5^{1.7}$

(b) $5^{1.73}$

(c) $5^{1.732}$

(d) $5^{\sqrt{3}}$

Step-by-Step Solution

Answer

The approximation of the numbers are 

(a) $5^{1.7}=15.426$

(b) $5^{1.73}=16.189$

(c) $5^{1.732}=16.241$

(d) $5^{\sqrt{3}}=16.241$

Part (a) Step 1. Given

The function $5^{1.7}$

To approximate the value.

Part (b) Step 2. Use the calculator and evaluate

By using the calculator,
$$\begin{gathered} 5^{1.7}=15.42584656 \\ =15.426 \end{gathered}$$

Part (b) Step 1. Given

The function $5^{1.73}$

To approximate the value.

Part (b) Step 2. Use the calculator and evaluate

By using the calculator, 

$$\begin{gathered} 5^{1.73}=16.18892859 \\ =16.189 \end{gathered}$$

Part (c) Step 1. Given

The function $5^{1.732}$

To approximate the value.

Part (c) Step 2. Use the calculator and evaluate

By using the calculator, 

$$\begin{gathered} 5^{1.732}=16.2411227 \\ =16.241 \end{gathered}$$

Part (d) Step 1. Given

The function $5^{\sqrt{3}}$

To approximate the value.

Part (d) Step 2. Use the calculator and evaluate

By using the calculator,

$$\begin{gathered} 5^{\sqrt{3}}=5^{1.732} \\ =16.2411227 \\ =16.241 \end{gathered}$$