Question

Find the square root of $1764$ by prime factorization method

Answer 1

Solve for the square root of given number:

Given number is $1764$

$\therefore$ The prime factorization of $1764$ can be written as

$$\begin{gathered} 1764=2\times 882 \\ =2\times 2\times 441 \\ =2\times 2\times 3\times 147 \\ =2\times 2\times 3\times 3\times 49 \\ =2\times 2\times 3\times 3\times 7\times 7 \end{gathered}$$

$\therefore 1764=2x2x3x3x7x7$

Taking square root on both sides

$\Rightarrow$$\sqrt{1764}=\sqrt{2x2x3x3x7x7}$

$\Rightarrow$$\sqrt{1764}=2x7x3$

$\therefore$$\sqrt{1764}=42$

Hence, the square root of $1764$ is $42$.