Q. 25 - Intermediate Algebra

Question

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

$ⓐ \sqrt{53} ⓑ \sqrt[3]{147} ⓒ\sqrt[4]{ 452}$

Step-by-Step Solution

Answer

Prat(a)$\sqrt{53}\approx 7.28$

Prat(b)$\sqrt[3]{101}\approx 5.28$

Prat(c)$\sqrt[4]{452}\approx 4.61$

Part(a) Step 1. Given information

(a)$\sqrt{53}$

Approximate each root and round to two decimal places.

Step 2. Explanaiton

Use the calculator square root key. 

$$\begin{gathered} \sqrt{53}=7.2801098892805 \\ \sqrt{53}\approx 7.28 \end{gathered}$$

Part(b) Step 3. Given information

(b)$\sqrt[3]{147}$

Approximate each root and round to two decimal places.

Step 4. Explanation

Use the calculator.

$$\begin{gathered} \sqrt[3]{101}=5.2776320879041 \\ \sqrt[3]{101}\approx 5.28 \end{gathered}$$

Part(c) Step 5. Given information

$ⓒ\sqrt[4]{ 452}$

Approximate each root and round to two decimal places.

Step 6. Explanation

Use the calculator.

$$\begin{gathered} \sqrt[4]{452}=4.6108883770342 \\ \sqrt[4]{452}\approx 4.61 \end{gathered}$$