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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. (i) 16562 (ii) 3698 (iii) 5103 (iv) 3174 (v) 1575 |
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Answer» (i) 16562 16562 = (7 × 7) × (13 × 13) × 2 \(\frac{16562}{2}\)= (7 × 7) × (13 × 13) \(\frac{16562}{2}\)= (7 × 13) × (7 × 13) = 91 × 91 = 912 Therefore, the resultant is the square of 91. ii) 3698 3698 = 2 × (43 × 43) \(\frac{3698}{2}\)= 43 × 43 = 432 Therefore, the numbers must be divided by 2 and resultant is square of 43. (iii) 5103 5103 = (3 × 3) × (3 × 3) × (3 × 3) × 7 \(\frac{5103}{7}\)= (3 × 3 × 3) × (3 × 3 × 3) = 27 × 27 = 272 Therefore, the number must be divided by 7 and resultant is square of 27. (iv) 3174 3174 = 2 × 3 × (23 × 23) \(\frac{3174}{6}\)= 23 × 23 = 232 Therefore, the number must be divided by 6 and the resultant is square of 23. (v) 1575 1575 = 3 × 3 × 5 × 5 × 7 \(\frac{1575}{7}\) = 3 × 3 × 5 × 5 = 15 × 15 = 152 Therefore, the number must be divided by 7 and the resultant is square of 15. |
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