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Maths-

General

Easy

Question

If N = 7^p+4.5^q.2³ is a perfect cube, where 'p' and 'q' are positive integers, the smallest possible value of 'p + q' is-

5
2
8
6

The correct answer is: 5

N = 7^{p +}⁴. 5^q.2³ is perfect cube.
7, 5, 2 has no common factor except '1'.
Least value of 'q' is 3 for which 5^q is cube.
Least value of 'p + 4' is '6' for which 7^p+4 is cube.
p + 4 = 6  p = 2
 Least value of p + q = 2 + 3 = 5.

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