Question

find the smallest number by which 3645 should be divided so as to get a perfect square also find the square root of the number so obtained​

Answer 1

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Answer 2

Answer:

Smallest number is 5 & root of the number is 27

Step-by-step explanation:

The prime factorisation of 3645:

3645 = 3 x 3 x 3 x 3 x 3 x 3 x 5

Grouping the factors into pairs of equal factors, we get:

3645 = (3 x 3) x (3 x 3) x (3 x 3) x 5

The factor, 5 does not have a pair. Therefore, we must divide 3645 by 5 to make a perfect square. The new number is:

(3 x 3) x (3 x 3) x (3 x 3) = 729

Taking one factor from each pair on the LHS, the square root of the new number is 3 x 3 x 3, which is equal to 27.