Question

Find the square root of $7056$ by prime factorization method

Answer 1

Solve for the square root of given number:

Given number is $7056$

By using the Prime factorization method, we get,

$$\begin{gathered} 7056=2\times 3528 \\ =2\times 2\times 1764 \\ =2\times 2\times 2\times 882 \\ =2\times 2\times 2\times 2\times 441 \\ =2\times 2\times 2\times 2\times 3\times 147 \\ =2\times 2\times 2\times 2\times 3\times 3\times 49 \\ =2\times 2\times 2\times 2\times 3\times 3\times 7\times 7 \end{gathered}$$

$\therefore 7056=2\times 2\times 2\times 2\times 3\times 3\times 7\times 7$

Applying square root on both sides,

$\Rightarrow \sqrt{7056}=\sqrt{2\times 2\times 2\times 2\times 3\times 3\times 7\times 7}$

$=2\times 2\times 3\times 7$

$=84$

Hence, the square root of $7056$ by using the prime factorization method is $84$.