Question

What is the square root of 122?
(a) $\sqrt{122}$
(b) $11\sqrt{2}$
(c) $2\sqrt{11}$
(d) None of these

Answer 1

Hint: In this problem, we are trying to find the square root of the given integer 122. First, we will factorize and find the square root of the term. Writing them in a proper form will give us our needed result.

Complete step by step solution:
According to the question, we are trying to find the square root of 122.
To find the square root of a given fraction we need to find square roots of the number after factoring.
We have our number as 122.
And we also see, $122=2\times 61$
Thus, the square root of 122 gives us, $\sqrt{122}=\sqrt{2\times 61}$ .
Now, we can see that both of the terms 2 and 61, are never repeating in the factorization; we can not take any one of them out of the root sign.
Then, the square root of 122 provides us, $\sqrt{122}=\sqrt{2\times 61}=\sqrt{122}$ .
Writing this into a fraction form, we are getting,$\sqrt{122}$.
Thus, we have our solution as, $\sqrt{122}$.
We have our solution as, (a) $\sqrt{122}$.

Note: There are lots of techniques to find the square root of a number. Some of them are listed below - 1. Prime Factorization Method and 2.Division Method. For the Prime Factorization Method, In this Method, we had to break down a number into its factors until all the numbers left are prime. We take the least factor. If we take the wrong factor then your answer would be incorrect.