Question

Find the square root of 144 by prime factorisation method.
(a) 12
(b) 11
(c) 10
(d) 9

Answer 1

Hint: For solving this question first, we will write the given number 144 into multiples of prime numbers and then apply the square root operator. After that, we will find the value of the square root of the number 144 easily and select the correct option.

Complete step-by-step answer:
Given:
We have to find the value of the square root of number 144 by prime factorisation method.
Now, before we proceed we should know that prime numbers are the numbers which are greater than 1 and have only two factors 1 and the number itself.
Now, first, we will write the given number 144 into multiples of prime numbers only. Then,
\[144=2\times 2\times 3\times 3\]
Now, from the above equation, we can find the value of the square root of number 144 easily. So, we will now find the square root of number 144. Then,
\[\begin{align}
  & 144=2\times 2\times 3\times 3 \\
 & \Rightarrow \sqrt{144}=\sqrt{2\times 2\times 3\times 3} \\
 & \Rightarrow \sqrt{144}=\sqrt{{{2}^{2}}\times {{3}^{2}}} \\
 & \Rightarrow \sqrt{144}={{2}^{2}}\times {{3}^{2}} \\
 & \Rightarrow \sqrt{144}=4\times 3 \\
 & \Rightarrow \sqrt{144}=12 \\
\end{align}\]
Now, from the result of the above calculation that we did, we can write that the value of the square root of the number 144 will be equal to 12.
Hence, option (a) will be the correct answer.

Note: Here, the student should first understand what is asked in the problem. Although the problem is very easy, we should solve it by the prime factorisation method only and while factorising the number 144 we should be careful and not miss any prime number while writing the number 144 into multiples of prime numbers. After that, we should apply the square root operator and find the value of the square root.