Question

Find the least numbr with which you mutiply 882 so that the product mayb a perfct square

Answer 1

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\underline{\large{\textsf{Step-1:}}}$
Express the number 882 as product of prime Factors

It can done using $\textsf{Prime Factorisation}$

$\begin{array}{r|l}2&882\\\cline{2-2}3&441\\\cline{2-2}3&147\\\cline{2-2}7&49\\\cline{2-2}7&7\\\cline{2-2}&1\\\end{array}$

$882 = 2 \times 3 \times 3 \times 7 \times 7$



$\underline{\large{\textsf{Step-2:}}}$
Pair the Prime factors considering 2 at a time

$882 = 2 \times 3^{2} \times 7^{2}$




$\underline{\large{\textsf{Step-3:}}}$
Note the unpaired prime factor(s)

In this case,
2 is not paired.

Unpaired prime factor is 2.



$\underline{\large{\textsf{Step-4:}}}$
Multiply the Non-perfect square with unpaired Prime factor to get perfect square.

The $\textsf{Unpaired prime Factor(or Product of Unpaired prime Factors)}$ is the $\textit{least number}$ which when Multiplied with a Non-perfect square results a Perfect square.

$882 \times 2 = 1764$

1764 is a perfect square.
It's square root = $2 \times 3\times7= 42$



$\therefore$

$\blacksquare\: \textsf{ Required Least Number = \underline{\large{\mathbf{2}}}}$