Question

The order and radicand of the surd $\sqrt[8]{12}$ are respectively-
A. 8, 12
B. 12, 8
C. 16, 12
D. 12, 16

Answer 1

Hint: The surd is essentially a symbol to represent the $n^{th}$ root of any positive real number. It consists of two parts- the order and the radicant. The surd can also be modified in the following way as-
$\sqrt[n]{x}=x^{{\displaystyle \frac{1}{n}}}$

Complete step-by-step answer:
We need to find the order and radicand of the given surd in this question. The order is the index of the root which needs to be calculated, and the radicand is the number of which we have to find the root. For example, in $\sqrt[4]{\text{x}+1}$, 4 is the order and (x + 1) is the radicand. This type of a surd is called a fourth order surd. Similarly, a surd with order n is called an $n^{th}$ order surd.
We have been given the surd $\sqrt[8]{12}$. The term inside the root is the radicand and the term outside is the order. So, in this case the order is 8 and the radicand is 12. Hence, the correct option for this question is A.

Note: A common mistake in this question is that students often exchange the values of the order and the radicand when they are in a hurry. Students should also remember this terminology of using surd, order and radicand as they are commonly used while describing roots of a number.