A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:
Let $ x $ = 6$ q $ + 3.
Then, $ x $2 = (6q + 3)2
= 36$ q $2 + 36$ q $ + 9
= 6(6 q 2 + 6$ q $ + 1) + 3
Thus, when $ x $2 is divided by 6, then remainder = 3.
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