Question

Which symbol denotes cube root?
A.$\sqrt[3]{{}}$
B.$\sqrt[{}]{{}}$
C.$\sqrt[5]{{}}$
D.$\sqrt[5]{{}}$

Answer 1

Hint: We can take the general representation of the nth root of a number. Then we can find what is the cube root. Then we can give the substitution for n and compare it with the option to find the required solution.

Complete step-by-step answer:
We need to find the symbol that represents the cube root.
We know that the cubic root of a number is the third root.
Now the nth root is represented by the symbol $\sqrt[n]{{}}$ .
Therefore, the third root is obtained by substituting $n = 3$ in the symbol that denotes the nth root. So we get the symbol as $\sqrt[3]{{}}$.
Therefore, the symbol which denotes the cube root is given by $\sqrt[3]{{}}$.
Thus, the required solution is $\sqrt[3]{{}}$.
So, the correct answer is option A.

Note: Alternative method to solve this problem is given by,
We know that a cube is a three-dimensional object which has all its sides equal. So, we can say that it is closely related to the number 3. Now we can check the option. By examining, we can say that only the symbol $\sqrt[n]{{}}$ has a 3 on it. So, we can conclude that the symbol which denotes the cube root is given by $\sqrt[3]{{}}$.
Thus, the required solution is $\sqrt[3]{{}}$.
So, the correct answer is option A.
We must note that $\sqrt[{}]{{}}$ has no numbers associated with it and it represents the 2nd root or square root. Cube root of a number can be defined as the side of the cube which has its volume equal to that number.