Question

What is the $4^{th}$ root of 16?
(a) 2
(b) 3
(c) 4
(d) None of these

Answer 1

Hint: In this problem, we are trying to find the 4^th root of a given number from the question. So, to find the solution, we can start by factoring it into prime factors. Then, while a term is multiplied 4 times is giving us our needed number, then we will get our result.

Complete step by step solution:
According to the problem, we are trying to find the 4^th root of 16.
So, to start with, we will have to try to factorize the given number 16.
Factoring 16, we are getting, $16=2\times 2\times 2\times 2$
Again, the fourth root of a number is the number that would have to be multiplied by itself 4 times to get the original number. Even for perfect fourth root numbers, the fourth root can be difficult to calculate by hand. The most basic techniques involve trial and error.
So, again, with the factorization of 16, we can see, multiplying 2, 4 times will give us the result 16.
Thus, it can be concluded that 2 is the fourth root of 16.
So, the correct answer is “Option a”.

Note: Keeping the roots in mind, finding the fourth root of a number is the opposite of multiplying a number by itself 4 times. In other words, it's the opposite of using an exponent of 4. And it is denoted by ${{x}^{\dfrac{1}{4}}}$ in the exponent form. This gives us the result of the fourth root of x.