Question

The square root of \[42\dfrac{{583}}{{1369}}\] is:
A \[6\dfrac{{19}}{{37}}\]
B \[4\dfrac{2}{{11}}\]
C \[7\dfrac{2}{{121}}\]
D None of these

Answer 1

Hint: In this problem, first we need to convert the given mixed fraction into fraction. Next, find out the square root of the obtained fraction. Now, again convert the obtained fraction into mixed fraction to get the final answer.

Complete step-by-step answer:
Rewrite the given mixed fraction into the fraction as shown below.

\[\begin{gathered}
  \,\,\,\,\,\,42\dfrac{{583}}{{1369}} \\
   \Rightarrow \dfrac{{1369 \times 42 + 583}}{{1369}} \\
   \Rightarrow \dfrac{{57498 + 583}}{{1369}} \\
   \Rightarrow \dfrac{{58081}}{{1369}} \\
\end{gathered}\]
Now, the square root of the above fraction can be calculated as follows:
\[\begin{gathered}
  \,\,\,\,\,\,\sqrt {\dfrac{{58081}}{{1369}}} \\
   \Rightarrow \dfrac{{\sqrt {58081} }}{{\sqrt {1369} }} \\
   \Rightarrow \dfrac{{\sqrt {241 \times 241} }}{{\sqrt {37 \times 37} }} \\
   \Rightarrow \dfrac{{241}}{{37}} \\
\end{gathered}\]
Now, rewrite the obtained fraction \[\dfrac{{241}}{{37}}\] into a mixed fraction as shown below.
\[\begin{gathered}
  \,\,\,\,\,\,\dfrac{{241}}{{37}} \\
   \Rightarrow 6\dfrac{{19}}{{37}} \\
\end{gathered}\]
Thus, the option (A) is the correct answer.

Note: In this problem, both numerator as well as denominator is square of prime numbers. The prime number is either divisible by 1 or itself.