Question

Find the least number with which 648 has to be multiplied to make it a perfect square

Answer 1

$Solution : \\ Prime \: \: factors \: \: of \: 648 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \\ Here, 2 \: \: has \: \: no \: \: pair. \\ So, it \: \: is \: \: not \: \: a \: \: perfect \: \: square.\\ Then, 648 \times 2 = {2}^{2} \times {3}^{2} \times {3}^{2} \times 2 \times 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} \times {3}^{2} \times {2}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1296 = {(36)}^{2} \\ which \: \: is \: \: a \: \: perfect \: \: square \: \: of \: 36. \\ Hence, the \: \: smallest \: \: number \: \: is \: \: 2 \: by \: \\ \: which \: 648 \: should \: \: be \: \: multiplied \: \: to \: \: get \: \: \\ a \: \: perfect \: \: square. \\ \\ \\ Hope \: \: it \: \: helps.$

Answer 2

Hello...
Answer...

Prime factors of 648 = 2*2*2*3*3*3*3
Here, 2 has no pair.

Then,648*2 = (2)^2*(3)^2*(3)^2*2*2
1296 = (36)^2

Now it is a perfect square of 36.

Hence, the smallest number which should be multiplied by 648 to get a perfect square is 2.

Hope it helped ☺☺☺