Question

6. Find the smallest number by which 8192 must be divided so that the quotient is a perfect cube. Also, find the cube root of the number thus obtained.​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Here, 8192 = 2×2×2×2×2×2×2×2×2×2×2 = 23 ×23 ×23×2 Since, one triples remain incomplete, hence 8192 is not a perfect cube. So, we divide 8192 by 2 to make its quotient a perfect cube. Since, 8192/2 = 4096 4096 = 2×2×2×2×2×2×2×2×2×2×2×2 = 23 ×23 ×23 ×23 Cube root of 4096, ∛4096 = ∛(23×23×23×23) = 2×2×2×2 = 16