Question

Using prime facterization find the smallest whole number, by which 396 should be multiplied so as to make it a perfect squar. Also find the sq root of the number so obtained



pls fast



with full explanation ​

Answer 1

Answer:

11

Step-by-step explanation:

By prime factorization of 396, we get

396 = 2 x 2 x 3 x 3 x 11

Here, 2 and 3 are in pairs, but 11 does not occur in pairs. Hence, the given number is not a perfect square.

Thus, 396 needs to be divided by 11 to become a perfect square.

396/11 = 2 x 2 x 3 x 3 x 11/11

36 = (2×2)×(3×3)

Thus, 36 has 2 pairs of equal prime factors. Hence, 36 is a perfect square & √36= 2×3= 6

 Thus, the required smallest whole number by which it should be divided so as to get a perfect square number is 11 and the square root is √36= 6.