Question

Find the square root of the following number by prime factorization method $1936$.

Answer 1

Step 1: Find the prime factors of the given number

The factors of $1936$ are

$$\begin{gathered} 1936=2\times 968 \\ =2\times 2\times 484 \\ =2\times 2\times 2\times 242 \\ =2\times 2\times 2\times 2\times 121 \\ =2\times 2\times 2\times 2\times 11\times 11 \end{gathered}$$

$\therefore 1936=2\times 2\times 2\times 2\times 11\times 11$

Step 2: Find the square root

The square root of $1936$ is

$$\begin{gathered} 1936=2\times 2\times 2\times 2\times 11\times 11 \\ \Rightarrow \sqrt{1936}=\sqrt{2\times 2\times 2\times 2\times 11\times 11} \\ \Rightarrow \sqrt{1936}=2\times 2\times 11 \\ \therefore \sqrt{1936}=44 \end{gathered}$$

Hence, the square root of $1936$ is $44$.