Question

Squaring both sides of an equation is irreversible. Is Cubing both sides of an equation reversible? Provide numerical examples to help support your answer.

Answer 1

Answer:

Cubing both sides of an equation is reversible.

Step-by-step explanation:

Squaring both sides of an equation is irreversible, because the square power of negative number gives a positive result, but you can't have a negative base with a positive number, given that the square root of a negative number doesn't exist for real numbers.

In case of cubic powers, this action is reversible, because the cubic root of a negative number is also a negative number. For example

$\sqrt[3]{x} =-1$

We cube both sides

$(\sqrt[3]{x} )^{3} =(-1)^{3} \\x=-1$

If we want to reverse the equation to the beginning, we can do it, using a cubic root on each side

$\sqrt[3]{x}=\sqrt[3]{-1} \\\sqrt[3]{x}=-1$

There you have it, cubing both sides of an equation is reversible.