Question

what should we multiply with 27to make it a perfect square​

Answer 1

Step-by-step explanation:

can be factored as 3 x 3 x 3, so another factor of 3 would be the smallest integer that would answer the question. After that, additional multipliers of already perfect squares will also work. Thus, to begin with 27 x 3 =81 = 9^2. Then,

27 x 3 x 4 = 27 x 12 = 324 = 18^2; 27 x 3 x 9 = 27 x 27 = 729 = 27^2; 27 x 3 x 16 = 1296 = 36^2; etc. If we don’t restrict ourselves to integer multipliers, other families of answers exists. For instance, 27 x 1/3 = 9 = 3^2; 27 x 1/27 = 1 = 1^2; 27 x 1/243 = 1/9 = (1/3)^2; etc. Also, by again including other perfect squares, we get the family

27 x 3/4 = 81/4 = (9/2)^2; 27 x 3/16 = 81/16 = (9/4)^2 and other similar families.