Question

How do you simplify $\sqrt {196} $?

Answer 1

Hint:
There are various methods which we can use for finding the square root of any number but the most easy and useful method is the factoring by squares in which we split a given number into the prime factor and make a square of every prime number. But here I have to write it in the simplified radical form.

Complete step by step solution:
According to the question we need to write $\sqrt {196} $ in the simplified radical form for we will use the same process as finding the square roots of any number.
So, we will split $196$ into prime numbers factor, now we will factorise it
We know that all numbers which has its last digit as number like $(1,2,3,4,.........)$ and we also know about the divisibility rules if any number’s last digit is $6$ and $0$ then it divided by the $2$ so now we will divide our given number by $2$ because our number is $196$ in which last digit is $6$
Now after dividing $196$ by $2$ we will get $98$
$ \Rightarrow 196 = 2 \times 98$
Now again we get $98$ which is also divisible by the $2$ after dividing we will get $49$
$ \Rightarrow 196 = 2 \times 2 \times 49$
Now we know that $49 = 7 \times 7$ so now we will write it as which is our final factor of $196$
So, our number is factorising and after factorising our number is in the prime factor and we get
$ \Rightarrow 196 = 2 \times 2 \times 7 \times 7$
Now we can see in above equation we have one pair of $2$ and other pair of $7$ now we can write it as
$ \Rightarrow \sqrt {196} = \sqrt {(2 \times 2) \times (7 \times 7)} $
And after solving it we will get $\sqrt {196} = (2 \times 7)$
So, our simplified radical form of the $\sqrt {196} $ is the $14$ which is our required answer of our question

Therefore the simplified radical form of the $\sqrt {196} $ is the $14$ which is our required answer.

Note:
There is no other method which is simple compared to this method. We have to solve our above question by this method because this method is very easy and quick and it is the basic if you want to solve any question then for any other question you can use it as it is. If your calculation is good then you can do it with a very quick method for solving these types of questions.