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126 = 2 × 3 × 3 × 7
= 2 × 32 × 7

In order for 126k to be a perfect square, we need to add one more “2” and one more “7”. This means that k = 2 × 7 = 14.

126k = 126 x 14
= 22 × 32 × 72

 

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