Common Algebra Mistakes
Example: Radical Expressions - Distance Formula

The Goal

Find the distance D between the points (x,0,0) and (x,y,z) in 3-space.

The Mistake

Find the algebra mistake:


(Roll the mouse over the algebra to see a hint in red)

The Correction


(Roll the mouse over the area above to see the correction in blue)

An Explanation

The mistake is in the final step - it is incorrect to distribute the square root over the sum. That is:


Try it with some numbers to convince yourself: let A=1 and B=1. The left side is √2, while the right side is 2. One counterexample disproves a general formula.

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