# 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.

**:**

__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.