A radical equation contains at least one term that's a square root, cube root, or some other root. When solving radical equations, you apply a method that's effective but comes with a built-in error possibility; you may find (and need to recognize) extraneous solutions. You need to rewrite absolute value equations to solve them. The solutions of the rewrites are then the solutions of the original equation.
Here's just a sampling of the radical things you work on in this chapter:
Here are a few things that may rock your boat, so be on the lookout:
686–689 Solve each radical equation by squaring both sides.
686.
687.
688.
689.
690–697 Solve the radical equations by squaring both sides; check for extraneous solutions.
690.
691.
692.
693.
694.
695.
696.
697.
698–701 Solve each radical equation by squaring both sides of the equation twice.
698.
699.
701.
702–703 Solve the radical equations.
702.
703.
704–713 Solve each absolute value equation by writing the two corresponding linear equations and solving.
704. |x + 3| = 8
705. |y − 4| = 3
706. |5z + 3| = 2
707. |3 − 2x| = 4
708. |4w − 1| − 6 = 9
709. 8 + |2 − w| = 10
710. 5|3x + 1| = 10
711. 3|x + 4| − 2 = 7
712. |−3x| = 4
713. |−2x − 3| = 15
714–715 Solve the absolute value equations, and check the answers carefully.
714. |3x − 2| + 4 = 1
715. 3 −|4 − 5x| = 7
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