Question

Find the square root of $6{\displaystyle \frac{115}{289}}$.
A.$2.410$
B.$2.529$
C.$2.113$
D.$2.482$

Answer 1

Hint: We have to find the square root of $6{\displaystyle \frac{115}{289}}$. Change mixed fraction to simple fraction and solve it.

Complete step-by-step answer:
Consider $x=6{\displaystyle \frac{115}{289}}$.
Now we have $6{\displaystyle \frac{115}{289}}$ so converting it into simple fraction we get,
$x={\displaystyle \frac{1849}{289}}$
So let us Square root of above we get,
$\sqrt{x}=\sqrt{{\displaystyle \frac{1849}{289}}}$ ……….. (1)
Now we know, ${(43)}^2=1849$ and ${(17)}^2=289$.
Now substituting above values in equation (1) we get,
 $\sqrt{x}=\sqrt{{\displaystyle \frac{{(43)}^2}{{(17)}^2}}}$
Simplifying in simple manner we get,
$\sqrt{x}={\displaystyle \frac{43}{17}}=2.529$
We get the square root of $6{\displaystyle \frac{115}{289}}$ is $2.529$.

Additional information:
The square root of any number is equal to a number, which when squared gives the original number. In order to calculate the square root, we first need to find the factors of a given number, then group the common factor together. Group the pairs separately if the factors have any perfect square. The square root of the square of a number is the number itself. If a number is a perfect square number, then there exists a perfect square root. To find the square root of any number, we need to figure out whether the given number is a perfect square or imperfect square. By using prime factorisation, we can find the square root of perfect squares. By using the long division method, we can find the square root of imperfect squares.


Note: A square root function is defined as a one-to-one function that takes a positive number as an input and returns the square root of the given input number. $f(x)=\sqrt{x}$. If a number is a perfect square number, then there exists a perfect square root. For example, if $x=9$, then the function returns the output value as $3$.