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Question:

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also, find the square root of the square number obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620

Solution:

i) 252 = 2 × 2 × 3 × 3 × 7
Therefore, we need to divide 252 by 7 in order to make it a perfect square.
So, 252/7 = 36 ∴ √36 = 6
ii) 2925 = 3 × 3 × 5 × 5 × 13
Therefore, we need to divide 2925 by 13 in order to make it a perfect square.
So, 2925/13 = 225 ∴ √225 = 15
iii) 396 = 2 × 2 × 3 × 3 × 11
Therefore, we need to divide 396 by 11 in order to make it a perfect square.
So, 396/11 = 36 ∴ √36 = 6
iv) 2645 = 5 × 23 × 23
Therefore, we need to divide 2645 by 5 in order to make it a perfect square.
So, 2645/5 = 529 ∴ √529 = 23
v) 2800 = 2 × 2 × 2 × 2 × 5 × 5 × 7
Therefore, we need to divide 2800 by 7 in order to make it a perfect square.
So, 2800/7 = 400 ∴ √400 = 20
vi) 1620 = 2 × 2 × 3 × 3 × 3 × 3 × 5
Therefore, we need to divide 1620 by 5 in order to make it a perfect square.
So, 1620/5 = 324 ∴ √324 = 18