Question

Question 91

Solve the following question:

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

a) 484
b) 11250
c) 841
d) 729

Answer 1

a) Prime factors of 484 $=(2\times 2)\times (11\times 11)$
As grouping, there is no unpaired factor left over.
$\begin{array}{cc}2& 484\\ 2& 242\\ 11& 121\\ 11& 11\\ & 1\end{array}$
So, 484 is a perfect square.

b) Prime factors of 11250 $=2\times (3\times 3)\times (5\times 5)\times (5\times 5)$
As grouping, 2 has no pair.
$\begin{array}{cc}2& 11250\\ 3& 5625\\ 3& 1875\\ 5& 625\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
So, 11250 is not a perfect square.

c) Prime factors of 841 $=(29\times 29)$
$\begin{array}{cc}29& 841\\ 29& 29\\ & 1\end{array}$
As grouping, there is no unpaired factor left over.
So, 841 is a perfect square.

d) Prime factors of 729 $=(3\times 3)\times (3\times 3)\times (3\times 3)$
As grouping, there is no unpaired factor left over.
$\begin{array}{cc}3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$
So, 729 is a perfect square.