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Ancient Greek's famous geometric problem is the doubling of the cube. It entail of constructing a cube with twice the volume as a given cube, using only a compass and straightedge. Using a mathematical approach to show it is impossible?

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Answer 1

Savannah Aguilar

It has been proven that no solution to this problem exists.

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Answer 2

Parker Allen

Using mathematical principles, it can be shown that it is impossible to double the volume of a cube using only a compass and straightedge. This is because the problem reduces to solving a cubic equation, specifically finding the cube root of 2. The cube root of 2 is an irrational number, meaning it cannot be expressed as a finite decimal or a fraction of two integers. Consequently, it cannot be constructed using only straightedge and compass, which are limited to creating lengths that are expressible as the square root of rational numbers. Therefore, the doubling of the cube cannot be achieved geometrically with the given tools.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.