Question

Find the square root of the following decimal number 18.49 .

Answer 1

Hint: For finding the square root, you must be thinking of 18.49 as a perfect square of what, small numbers like 36, 49 you can guess but the number like 18.49 needs a complex method. So, here we are using a long division method to find the square root of 18.49.

Complete step-by-step answer:
In the long division method, we divide the number into two halves. Here in 18.37 first we divide 18 by a number whose square is less than or equal to 18 then what we got as a remainder, we will club with the subsequent number 49 then the new number that we have got after clubbing is 249.
Now, we will divide this 249 number by a number 83. The question that will pop here is, how we are getting 83 so the answer is: first we add 4 by itself, what we get is 8 then we will put another number say “x” which is at unit place and 8 will be at tens place so this 8x number is multiplied by “x”. So, how we get this “x”? “x” could be any whole number, we have to do the hit and trial method to find the suitable “x” in which 8x on multiplication with x is yielded to 249.
$\dfrac{4}{83}\left| \begin{align}
  & 18.49 \\
 & \dfrac{16.00}{0249} \\
 & \dfrac{0249}{0000} \\
\end{align} \right|4.3$
Hence, the square root of 18.49 is 4.3.

Note: You might think prime factorization could be a possible method to find the square root of this decimal number but when you start to factorize then you will see that 18.49 is not passing the divisibility rule from 2to9 and even after 9 so it could be very time consuming process to check numbers like that. So, this long division method that I have shown above is a better method than prime factorization.