In a military camp the major has to arrange 1764 soldiers in a square shape such that the number of soldiers along the length and breadth are equal. How many soldiers are there in each raw ?

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Solution:

⇨The prime factors of 1764 by prime factorization method are

1764 = 2 x 2 x 3 x 3 x 7 x 7

⇨ 1764 = 2^2 x 3^2 x 7^2

⇨ 1764 = (2 x 3 x 7)^2

⇨ 1764 = (42)^2

⇨Therefore there are 42 soldiers in each raw