Question

find the smallest no. by which 3645 must be divided so that it becomes a perfect square. also find the sq. root of resulting no.​

Answer 1

Answer:

Step-by-step explanation:

first we will take out the prime factorization of the no.

            5 | 3645

            3  | 729

            3  | 243

            3  | 81

             3 |  9

             3  | 3

             3   |  1

so 3645=5*3*3*3*3*3*3

now we will pair up each of the factors in groups of two

so 3645 = 5 * (3*3)*(3*3)*(3*3)

now we will see if any one is not pair . here we come to know that 5 is not paired so we will come to a conclusion that if we divide 5 with the number then 5 will  not be there resulting in a perfect square and so we will get a square number as  in each pair the same no. are being multiplied so it will lead us to a perfect square if we divide 5 with the number.

when we divide five with the no. 3645 we get

3645/5 =729

prime factoras of 729 can be predicted without doing actual factorization because we just divided five to the prime factors of 366455.

so ,

729=(3*3)*(3*3)*(3*3)

so therefore ,729 is a perfect square of 3*3*3 = 27