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प्रश्न
Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers.
उत्तर
10368 = `bar(2xx2) xx bar(2xx2) xx bar(2xx2) xx2 xx bar(3xx3) xx bar(3xx3)`
On grouping the prime factors of 10368 as shown; one factors i.e. 2 is left which cannot be paired with equal factor.
| 2 | 10368 |
| 2 | 5184 |
| 2 | 2592 |
| 2 | 1296 |
| 2 | 648 |
| 2 | 324 |
| 2 | 162 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 |
∴ The given number should be divided by 2.
Now `sqrt(10368/2)`
= `sqrt((bar(2xx2) xxbar(2xx2) xx bar(2xx2) xx2 xx bar(3xx3) xx bar(3xx3))/(2)`
= 2 x 2 x 2 x 3 x 3 = 72
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