4.Find the smallest number by which 3645 must be divided so that it becomes a
perfect square. Also, find the square root of the resulting number.
5.A gardener planted 1,521 trees in rows such that the number of rows was equal to
the number of plants in each row. Find the number of rows.
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4. The smallest number divided is 5.
5. 39 number of rows.
Step-by-step explanation:
4. L.C.M of 3645 = 5 × 3 × 3 × 3 × 3 × 3 × 3
Form as a pair with same number:
5 × 3 × 3 × 3 × 3 × 3 × 3 = 5 × (3 × 3) × (3 × 3) × (3 × 3)
Prime factor 5 is only alone, so divide it.
3645/5 = 5 × (3 × 3) × (3 × 3) × (3 × 3)/5
729 = (3 × 3) × (3 × 3) × (3 × 3)
Make the pair in 1 number:
729 = 3 × 3 × 3
√729 = 27
∴The smallest number divided is 5.
5. No. of rows = No. of plants in each row
No. of trees planted = 1521
x² = 1521
x = √1521
x = 39
∴ 39 number of rows.
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