Question

if the value of the expression 576 x a is a perfect cube, then what is the least possible value of a perfect cube,then what is the last possible value of a

Answer 1

Hey friend, Harish here.

Here is your answer.

Given that 576 × a 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 a perfect cube (i.e 4³ ) but 3² is not a perfect cube.

So for making it a perfect cube the minimum value of a must be 3.

Because ( 4³ × 3² ) × a = ( 4³ × 3² ) × 3 = ( 4³ × 3³ ) = ( 4 × 3 )³ = (12)³.

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Hope my answer is helpful to you.

Answer 2

The least value of a = 3

And the possible least perfect cube = 1728

Given:

The value of the expression 576 x a is a perfect cube

To find:

what is the least possible value of a perfect cube,then what is the last possible value of a

Solution:

Perfect cube is a number which can be written in the form of a³ or which can be written as triplet multiple of itself

Given 576 x a is a perfect cube

Now write 576xa as product of its Prime factors

576 x a = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × a

Now group the above factor as triplets

2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × a = (2×2×2) × (2×2×2) × 3 × 3 × a  

= 2³ × 2³ × 3 × 3 × a

Here 3 are left

So to make 576xa, we need one more 3

The least value of a = 3

And the possible least perfect cube = 1728

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