Question

How do you find the square root of $ \dfrac{{92}}{{207}} $ ?

Answer 1

Hint: In the question, we are given a fraction whose square root we have to find, for finding the square root, we will first simplify the fraction. When a number is multiplied with itself, we get the square of that number. Thus, the square root is defined as the number whose square we found.

Complete step-by-step answer:
Now, we have to find the square root of the simplified fraction, that is, we have to find the number whose square is equal to $ \dfrac{{92}}{{207}} $ . So for that, we write the numerator and the denominator as a product of its prime factors and then see them individually if they can be written as a square of any number. Thus, after writing the given fraction as a square of a number, we can find out its square root.
On the factorization of 92 and 207, we get –
 $
  92 = 2 \times 2 \times 23 = {2^2} \times 23 \\
  207 = 3 \times 3 \times 23 = {3^2} \times 23 \;
  $
Now, the numerator and the denominator have 23 as the common factor so it is canceled out
 $ \Rightarrow \sqrt {\dfrac{{92}}{{207}}} = \sqrt {\dfrac{{2 \times 2}}{{3 \times 3}}} = \pm \dfrac{2}{3} $
Hence, the square root of $ \dfrac{{92}}{{207}} $ is $ \pm \dfrac{2}{3} $ .
So, the correct answer is “ $ \pm \dfrac{2}{3} $ ”.

Note: The question is given in fraction form which has two parts, the upper part called the numerator and the lower part called the denominator, they both are separated by a horizontal line. For simplifying a fraction, we have to write the numerator and the denominator of a fraction as a product of its prime factors and then divide both the numerator and the denominator by their common factor. But in the fraction obtained after square rooting the given fraction, the numerator and the denominator are already prime factors so the given fraction is already simplified and thus cannot be simplified further.