Assignment:
In solving an equation involving radicals, it is sometimes necessary to square each side of the equation. But doing this can introduce extraneous roots, which do not satisfy the original equation. After squaring both sides, when you then take the square root of both sides again, you do not get back the original equation exactly. There is a 'loss of information' when both sides of an equation are squared. Can you explain the origin of this phenomenon?
Provide complete and step by step solution for the question and show calculations and use formulas.