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Question

If 2904q is a perfect square, write down the smallest integer value of q.

Answer

Just remember the prime numbers: 2, 3, 5, 7, 11, 13, 17, 19…

2,904 = 2 x 1,452
= 2 x 2 x 726
= 2 x 2 x 2 x 363
= 2 x 2 x 2 x 3 x 121
= 2 x 2 x 2 x 3 x 11 x 11

We need 1 more 2 and 1 more 3 to make all the factors perfect squares, so…

2 x 3 = 6


Check

2,904 x 6 = 17,424

2 x 2 x 2 x 2 x 3 x 3 x 11 x 11
= (2 x 2 x 3 x 11)2
= (132)2
= 17,424

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