Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Arrange the following in ascending order of magnitude:
[tex]\(\sqrt[3]{3}, \sqrt[3]{4}, \sqrt[3]{2}\)[/tex]

Arrange the following in descending order of magnitude:
[tex]\(\sqrt[8]{90}, \sqrt[7]{10}, \sqrt{6}\)[/tex]

Sagot :

GinnyAnswer
Sure, let's break down the problem step by step.

First, we will address arranging the given numbers in ascending order of magnitude:
- The numbers to be arranged are [tex]\(\sqrt[3]{3}, \sqrt[3]{4}, \sqrt[3]{2}\)[/tex].

To solve this, we evaluate these cube roots:
1. [tex]\(\sqrt[3]{2}\)[/tex] approximately equals [tex]\(1.2599210498948732\)[/tex],
2. [tex]\(\sqrt[3]{3}\)[/tex] approximately equals [tex]\(1.4422495703074083\)[/tex],
3. [tex]\(\sqrt[3]{4}\)[/tex] approximately equals [tex]\(1.5874010519681994\)[/tex].

Now, we sort these values from smallest to largest:
- [tex]\(1.2599210498948732\)[/tex] corresponding to [tex]\(\sqrt[3]{2}\)[/tex],
- [tex]\(1.4422495703074083\)[/tex] corresponding to [tex]\(\sqrt[3]{3}\)[/tex],
- [tex]\(1.5874010519681994\)[/tex] corresponding to [tex]\(\sqrt[3]{4}\)[/tex].

Therefore, the ascending order is:
1. [tex]\(\sqrt[3]{2}\)[/tex],
2. [tex]\(\sqrt[3]{3}\)[/tex],
3. [tex]\(\sqrt[3]{4}\)[/tex].

Next, we will address arranging the given numbers in descending order of magnitude:
- The numbers to be arranged are [tex]\(\sqrt[8]{90}, \sqrt[7]{10}, \sqrt{6}\)[/tex].

To solve this, we evaluate these roots:
1. [tex]\(\sqrt{6}\)[/tex] (square root of 6) approximately equals [tex]\(2.449489742783178\)[/tex],
2. [tex]\(\sqrt[7]{10}\)[/tex] (seventh root of 10) approximately equals [tex]\(1.3894954943731377\)[/tex],
3. [tex]\(\sqrt[8]{90}\)[/tex] (eighth root of 90) approximately equals [tex]\(1.7550129025853407\)[/tex].

Now, we sort these values from largest to smallest:
- [tex]\(2.449489742783178\)[/tex] corresponding to [tex]\(\sqrt{6}\)[/tex],
- [tex]\(1.7550129025853407\)[/tex] corresponding to [tex]\(\sqrt[8]{90}\)[/tex],
- [tex]\(1.3894954943731377\)[/tex] corresponding to [tex]\(\sqrt[7]{10}\)[/tex].

Therefore, the descending order is:
1. [tex]\(\sqrt{6}\)[/tex],
2. [tex]\(\sqrt[8]{90}\)[/tex],
3. [tex]\(\sqrt[7]{10}\)[/tex].

So, summarizing:
- The ascending order for [tex]\(\sqrt[3]{3}, \sqrt[3]{4}, \sqrt[3]{2}\)[/tex] is: [tex]\(\sqrt[3]{2}, \sqrt[3]{3}, \sqrt[3]{4}\)[/tex].
- The descending order for [tex]\(\sqrt[8]{90}, \sqrt[7]{10}, \sqrt{6}\)[/tex] is: [tex]\(\sqrt{6}, \sqrt[8]{90}, \sqrt[7]{10}\)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.