Question

Find the smallest number by which 98 should be multiplied to make it a perfect square.

Answer 1

Hint: First, we will find factors of 98 which are given as ‘numbers on multiplying gives the original number’. For example: to get number 15, factors are 3 and 5. On multiplying 3 and 5, we get 15. Then we will select the smallest number from factors obtained and multiply it to 98, to see that number is a perfect square or not. If yes, we will get the answer.

Complete step-by-step answer:
Here, we have to first find factors of 98. Factors are obtained by dividing 98 by 2, 3, 4, … . So, on doing this we get as
 $ \begin{align}
  & 2\left| \!{\underline {\,
  98 \,}} \right. \\
 & 2\left| \!{\underline {\,
  49 \,}} \right. \\
 & 7\left| \!{\underline {\,
  7 \,}} \right. \\
\end{align} $
So, factors of 98 are $ 98=2\times 7\times 7 $ . Now, we can see that out of 2 and 7 the smallest number is 2. We will select the smallest number from factors obtained and multiply it to 98, to see that number is a perfect square or not. If yes, we will get the answer.
So, on multiplying 98 to 2, we get $ 98\times 2=196 $ .
Thus, 196 is the perfect square of number 14.
Hence, the smallest number by which 98 should be multiplied to make it a perfect square is 2.

Note: Students generally make mistakes by assuming that 100 is a perfect square near to 98. So, we will find out on multiplying which number we will get an answer to be 100. So, the equation will be $ 98\times x=100 $ . On solving, we get x as $ x=\dfrac{100}{98}=1.020 $ and write this answer. But this number is in decimal form and is a totally incorrect answer. We have to find integer value and not decimal value. So, be careful in this type of problem.