6. By what numbers should each of the
following be divided to get a perfect
square in each case? Also find the number
whose square is the new number?
(1) 1575
(ii) 3174 (iii) 5103
(iv) 3698
(v) 16562
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Answer:
For a number to be a perfect square, each prime factor has to be paired. Hence, 3174 must be divided by 6 (2 x 3) for it to be a perfect square. The new number would be (23 x 23). Hence, the number whose square is the new number is 23.
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