Solution
1) we need to compare the following values:
![5.6,\sqrt[]{27}](https://img.qammunity.org/2023/formulas/mathematics/college/esvs507e77rrwk0ayxu7g1y7r6yvnwoyf9.png)
We can write square root of 27 like this:
![\sqrt[]{27}=\sqrt[]{9\cdot3}=3\sqrt[]{3}=5.196](https://img.qammunity.org/2023/formulas/mathematics/college/jq02lytvv5yemd7kfzsxft7exbu761rw6h.png)
So then we can conclude that:
![5.6>\sqrt[]{27}](https://img.qammunity.org/2023/formulas/mathematics/college/9dverzsro32xlpqrnhmu0kn4w42nrbt5a0.png)
2) We have the following numbers :
![\frac{8}{\sqrt[]{65}},\frac{5}{\sqrt[]{65}}](https://img.qammunity.org/2023/formulas/mathematics/college/xvqacemww8ifrri4qjermyf6q17iwnh5ra.png)
By direct comparison we see that we have the same denominator and 8>5 so then we can conclude this:
![\frac{8}{\sqrt[]{65}}>\frac{5}{\sqrt[]{65}}](https://img.qammunity.org/2023/formulas/mathematics/college/8p7bz32smcodsouxq916pq1k40w77r6ekc.png)