Question

What is the square root of $\dfrac{25}{36}$ ?
(a) $\dfrac{5}{2}$
(b) $\dfrac{1}{2}$
(c) $\dfrac{5}{6}$
(d) None of these

Answer 1

Hint: In this problem, we are trying to find the square root of the given fraction $\dfrac{25}{36}$. To find the square root, we will find the square root of the denominator and numerator differently. First we will try to factorize the terms in the denominator and numerator. Thus, we will factorize and find the square root of each of them. Writing them in a fraction 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 $\dfrac{25}{36}$.
To find the square root of a given fraction we need to find square roots of the denominator and the numerator separately.
We have our numerator as 25.
And we also see, $25=5\times 5$
Thus, the square root of 25 gives us, $\sqrt{25}=5$ .
Again, we also have our denominator as 36.
We also see that, $36=6\times 6$
Then, the square root of 36 provides us, $\sqrt{36}=6$ .
Writing this into a fraction form, we are getting, $\dfrac{5}{6}$ .
Thus, we have our solution as, \[\sqrt{\dfrac{25}{36}}=\dfrac{5}{6}\].

So, the correct answer is “Option c”.

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.