Question

What is the square root of $98?$

Answer 1

Hint: We have to find the square root of $98$ . We solve this question by resolving the value $98$ into prime factors . The square root of a number is represented as the value of another number when it is multiplied by itself gives the value of as the original number . After finding the prime factors we can calculate the value of a square root . If a prime factor is left single or in odd factor terms then we can calculate it using the table method of square root .

Complete step-by-step answer:
Given : we have to find $(\sqrt {98} )$
To find the square root using prime factorisation method , we resolve the original number into prime factors
So , prime factors of $98$ in table form
\[98{\text{ }} = {\text{ }}2{\text{ }} \times {\text{ }}49\]
\[49{\text{ }} = {\text{ }}7{\text{ }} \times {\text{ }}7\]
\[7{\text{ }} = {\text{ }}7{\text{ }} \times {\text{ }}1\]
Hence the prime factors of $98$ are\[2{\text{ }},{\text{ }}7{\text{ }},{\text{ }}7\].
As $98$ has a factor of $7$ two times , so
In the value of square root it will give only one $7$
$98 = {7^2} \times 2$Square root of $98 = 7 \times \sqrt 2 $
Now , we have to find the square root of $2$
Also , we know
$\sqrt 2 = 1.41421$
Now ,
$\sqrt {98} = 7 \times 1.41421$
$\sqrt {98} = 9.89947$
Thus the square root of \[98{\text{ }} = {\text{ }}9.8995\]
So, the correct answer is “9.8995”.

Note: A square root number can be a rational or irrational number . If square root of a number can be represented in terms of natural number than it is a rational number i.e. it can be written in the form of $\dfrac{p}{q}$where\[q{\text{ }} \ne {\text{ }}0\]. And if square root of a number can not be represented in terms of natural number than it is an irrational number i.e. it can be written in the form of $\dfrac{p}{q}$ where \[q{\text{ }} \ne {\text{ }}0{\text{ }}.\]