Question

if a, b, c and d are four odd perfect cube number then which of the following are always a factor of
$(3 \sqrt{a + 3 \sqrt{b)2(3 \sqrt{c + 3 \sqrt{d)} } } }$

Answer 1

Thank you for asking this question. Here is your answer:

a = 1

b = 8

c = 125

d = 343

These are the four odd perfect cube numbers.

∛a=∛1=1,∛b=∛8=2,∛c=∛125=5  and ∛d=∛343=7  

(∛a+∛b)^2 (∛c  ∛d) will be 192, 360, 512, 576 and 600

(192, 360, 512, 576, 600) = 8

So this means that 8 will always be the factor of (∛a+∛b)^2 (∛c+∛d)

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