Algebra

Losing Solutions When Squaring Both Sides

Students square both sides or take square roots and keep only the positive case, so they drop a valid solution.

Quick check

Why students make it

The square root symbol gives the principal nonnegative root, so students think a squared expression has only one undoing. They forget that two opposite numbers can have the same square.

The rule done right

Use A2=∣A∣\sqrt{A^2}=|A|, not AA. If A2=B2A^2=B^2, then solve A=BA=B and A=−BA=-B, then check any solutions in the original equation.

Related resources

quadraticssquare-rootsabsolute-value