In this lesson, students continue to investigate solutions to equations that involve squares and square roots. In particular, they find that squaring each side of an equation may result in a new equation that has solutions that are not solutions to the original equation. They also recall that taking the square root of each side of an equation runs the risk of ignoring some solutions, as first discussed in a previous course. The key idea is to think carefully about solutions when using squares or square roots to solve an equation.

There are two optional activities in this lesson. The first is optional practice that shows an alternate way of solving these equations. Consider using it if students need additional support in understanding why quadratic equations often have two solutions. The section provides extra practice with solving square root equations that all classes may not need.

Students reason abstractly and quantitatively when they analyze possible solutions to equations involving squares and square roots (MP2).