Q. 26 - Intermediate Algebra

Question

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

$ⓐ \sqrt{47} ⓑ \sqrt[3]{163} ⓒ \sqrt[4]{527}$

Step-by-Step Solution

Answer

Part(a)$\sqrt{47}\approx 6.85$

Part(b)$\sqrt[3]{163}=5.46$

Part(c)$\sqrt[4]{527}\approx 4.79$

Part(a) Step 1 Given information

$ⓐ \sqrt{47}$

Approximate each root and round to two decimal places.

Step 2 Explanation

Use the calculator square root key. 

$$\begin{gathered} \sqrt{47}=6.855654600401 \\ \sqrt{47}\approx 6.85 \end{gathered}$$

Part (b) Step3 Given information

$ⓑ \sqrt[3]{163}$

Approximate each root and round to two decimal places.

Step 4. Explanation

Use the calculator cube root key. 

$$\begin{gathered} \sqrt[3]{163}=5.4625555712814 \\ \sqrt[3]{163}=5.46 \end{gathered}$$

Part (c) Step 5. Given information

$ⓒ \sqrt[4]{527}$

Approximate each root and round to two decimal places.

Step 6. Explanation

Use the calculator 

$$\begin{gathered} \sqrt[4]{527}=4.7912921604196 \\ \sqrt[4]{527}\approx 4.79 \end{gathered}$$