Question

The product of (-576× x) is a perfect cube. What is the least possible value of 'x'

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Answer 1

Answer:

576×(−3)= –1728

cuberoot of –1728=12

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Answer 2

Answer:

given that 576 × x must be a perfect square

now let us factor 576 which is done as;

576= 2⁶×3²= 4³×3²

we can notice that 576 already has the perfect cube(i.e.4³) but 3² is not a perfect cube

so for making it a perfect cube the minimum value of x must be 3

because(4³× 3²)×x =(4³×3²)×3=(4³×3³)= (4×3)³= (12)³