Q. 23 - Intermediate Algebra

Question

In the following exercises, approximate each root and round to two decimal places. 

ⓐ $\sqrt{19}$ ⓑ $\sqrt[3]{89}$ 3 ⓒ $\sqrt[4]{ 97 }$

Step-by-Step Solution

Answer

Part(a)$\sqrt{19}\approx 4.36$

Part(b)$\sqrt[3]{89}\approx 3.65$

Part(c)$\sqrt[4]{97}\approx 3.14$

Part(a) Step 1. Given inforamtion

(a) $\sqrt{19}$

Approximate each root and round to two decimal places.

Step 2. Explanation

Use the calculator square root key. 

$\sqrt{19}=4.358898$

Round to two decimal places. 

$$\begin{gathered} \Rightarrow 4.36 \\ \sqrt{19}\approx 4.36 \end{gathered}$$

Part (b) step 3. Given information

 (b) $\sqrt[3]{89}$

Approximate each root and round to two decimal places.

Step 4. Explanaiton

Use the calculator.

$$\begin{gathered} \sqrt[3]{89}==3.65930571 \\ \sqrt[3]{89}\approx 3.65 \end{gathered}$$

Part (c) Step 5 Given inforamtion

(c)$\sqrt[4]{97}$

Approximate each root and round to two decimal places.

Step 6. Explanation

Use the calculator 

$\sqrt[4]{97}=3.13828899$

Round to two decimal places. 

$\sqrt[4]{97} \approx 3.14$