Question

State the order of the surd :
1. $\sqrt[3]{5}$
2. $\sqrt[4]{8}$?

Answer 1

Hint: To find the order of the surd, you first need to find the index of the root for which you want to find the order. The index of the root is the value which is on the left side of the square root on the outside. For example to find the surd of the square root $\sqrt[3]{5}$, you need to find the index. In this example the index is 3. Therefore, the order is 3.

Complete step by step solution:
Here is the complete step by step solution.
The first step we need to do is to find the index of the square root. The index of the square root is the number which is on the outside of the square root . Therefore, for finding the surd for the following square roots, we first need to find the index.
This index is the order of the surd.
The index for $\sqrt[3]{5}$ is 3. Therefore, the order is 3.
The index for $\sqrt[3]{5}$ is 4. Therefore, the order is 4.
Therefore, as we can see , we get the final answer for the question as , the order for the first surd is 3 and the order for the second surd is 4.

Note: This question does not require any formulas. You just need to remember what an index of a square root is and what the order of surd means. You can also write a square root in terms of power of something like, this $\sqrt[3]{5}$ can be written as $5^{\dfrac{1}{2}}$ .