Question

Find the square root of the \[196\] by factorization.

Answer 1

Hint: The factors any of the prime numbers that can be multiplied to give the original number is called prime factors. First we have to calculate the prime factors of \[196\] by dividing the number with its prime factors like \[7\] and \[2\]. Then we have to find the number which produces a specified quantity when multiplied by itself.

Complete step-by-step answer:
We know factors of a number are numbers that divide evenly into another number. Factorization writes a number as the product of smaller numbers.
We have to find the square root of 196 by factorization.
The most common way is to divide the number by its prime divisors until only the number 1 is left. Here \[2\] and \[7\] are the prime numbers we can use as prime factors of the digit \[196\].
Now for the factorization part,
\[\begin{align}
  & 2\left| \!{\underline {\,
  196 \,}} \right. \\
 & 2\left| \!{\underline {\,
  98 \,}} \right. \\
 & 7\left| \!{\underline {\,
  49 \,}} \right. \\
 & 7\left| \!{\underline {\,
  7 \,}} \right. \\
 & \text{ }1 \\
\end{align}\]

We know that a square root of a number is a value that, when multiplied by itself, gives the number. For example \[4\times 4=16\]. So a square root of 16 is 4.
Now we can write the prime factors under square root, as we have to evaluate the square root of that number.
\[\begin{align}
  & \sqrt{2\times 2\times 7\times 7} \\
 & \Rightarrow \sqrt{{{2}^{2}}\times {{7}^{2}}} \\
 & \Rightarrow \sqrt{{{14}^{2}}} \\
 & \Rightarrow 14 \\
\end{align}\]

The square root of the \[196\] is \[14\].

Note: We have to remember while factorization we always have to take prime factors. If we take non-prime numbers as a factor at first then we have to face problems later in the square root section. We can use prime factors like 7 in first then 2 in the process of calculation.