
Find the smallest number by which 98 should be multiplied to make it a perfect square.
Answer
484.5k+ views
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.
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.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
When people say No pun intended what does that mea class 8 english CBSE

How many ounces are in 500 mL class 8 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which king started the organization of the Kumbh fair class 8 social science CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Advantages and disadvantages of science
