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प्रश्न
By what number should each of the following numbers be multiplied to get a perfect square ? Also, find the number whose square is the new number.
3468
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उत्तर
3468 = 2 x 2 x 3 x 17 x 17
Grouping them into pairs of equal factors:
3468 = (2 x 2) x (17 x 17) x 3
The factor 3 is not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 3468 must be multiplied by 3 for it to be a perfect square.
The new number would be (2 x 2) x (17 x 17) x (3 x 3).
Furthermore, we have:
(2 x 2) x (17 x 17) x (3 x 3) = (2 x 3 x 17) x (2 x 3 x 17)
Hence, the number whose square is the new number is:
2 x 3 x 17 = 102
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