Question

Determine whether $441$ is a perfect square using prime factorization.

• A. Yes, $441$ is a perfect square.
• B. No, $441$ is a not perfect square.

Answer 1

The correct option is A Yes, $441$ is a perfect square.

Let's find out the factors of $441.$

Sum of the digits, $4+4+1,$ is $9.$
$\therefore 441$ is divisible by $9.$
$\Rightarrow 441=9\times 49$
$\Rightarrow 441=3\times 3\times 7\times 7$
This is the prime factorization of $441.$
$\Rightarrow 441=(3\times 7)\times (3\times 7)$
$\Rightarrow 441=(3\times 7{)}^2$
$\Rightarrow 441=(21{)}^2$

$\therefore 441$ is a perfect square of $21.$