Question

which is the smallest number that can be multiplied to 10400 to give a perfect square​

Answer 1

2 |10400

2 |5200

2 | 2600

2 |1300

2 |650

5 |325

5 |65

|13

$10400 = {2}^5 \times {5}^{2} \times 13$

So as to become a perfect square we need to multiply by 2 and then by 13, we get

${2}^6 \times {5}^{2} \times {13}^{2}$

So it needs to multiply by 26 to get a perfect square. Hope it helps you.