Question

Find the square root of $324$ using prime factorization.

• A. $16$
• B. $17$
• C. $18$
• D. $19$

Answer 1

The correct option is C $18$

$324$ is divisible by $9$ as the sum of the digits is $9.$
$\frac{324}{9}=36$
$\therefore 324=9\times 6\times 6$
$\Rightarrow 324=(3\times 3)\times (2\times 3)\times (2\times 3)$
$\Rightarrow 324=(3\times 3\times 2)\times (3\times 3\times 2)$
$\Rightarrow 324=(3\times 3\times 2{)}^2$
$\Rightarrow 324=(18{)}^2$
$\Rightarrow \sqrt{324}=18$