Question

Using prime factorization, find which of the following are perfect squares.

$\left(a\right)484$

Answer 1

Solution.

First, find the factors by using the prime factorization method.

$$\begin{gathered} 2|484 \\ 2|242 \\ 11|121 \\ 11|11 \\ |1 \end{gathered}$$

$\therefore 484=2\times 2\times 11\times 11$

If after the pairing of resulting factors, no unpaired factor is left. Then, the number will be a perfect square.

$\therefore 484=(2\times 2)\times (11\times 11)$

Here, after pairing, no unpaired factor is left.

Hence, the given number is a perfect square.