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

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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.

\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 $98\times 2=196$ .
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.