To determine the order of the surds given, you need to identify the root's degree for each expression. The order of a surd tells us whether it is a square root, cube root, fourth root, etc. Here’s how you can identify the order step-by-step:
### 1) [tex]\(\sqrt[3]{17}\)[/tex]
1. Identify the expression: [tex]\(\sqrt[3]{17}\)[/tex].
2. Notice that the number in the root symbol's index (above the radical sign) is [tex]\(3\)[/tex].
3. The index indicates the root's degree. In this case, it is [tex]\(3\)[/tex].
4. Therefore, the order of the surd [tex]\(\sqrt[3]{17}\)[/tex] is 3.
### 2) [tex]\(\sqrt[4]{10}\)[/tex]
1. Identify the expression: [tex]\(\sqrt[4]{10}\)[/tex].
2. Notice that the number in the root symbol's index (above the radical sign) is [tex]\(4\)[/tex].
3. The index indicates the root's degree. In this case, it is [tex]\(4\)[/tex].
4. Therefore, the order of the surd [tex]\(\sqrt[4]{10}\)[/tex] is 4.
### Conclusion:
- The order of the surd [tex]\(\sqrt[3]{17}\)[/tex] is 3.
- The order of the surd [tex]\(\sqrt[4]{10}\)[/tex] is 4.
The numerical results, hence, are:
- For the expression [tex]\(\sqrt[3]{17}\)[/tex], the order is 3.
- For the expression [tex]\(\sqrt[4]{10}\)[/tex], the order is 4.
