Solve simple rational and radical equations and identify extraneous solutions.
Solve a square-root equation with one radical and check for extraneous solutions
Problem
Solve \(\sqrt{x~+~5}~=~4\) and verify the result in the original equation.
Big Picture
What this problem is really about
First note the radical's real-number domain and isolate the square root if necessary. Squaring both sides removes the principal square root, but it can also broaden the equation and create candidates that were never valid originally. Solve the transformed equation, then substitute every candidate into the unsquared equation; that final check, not the squared work alone, determines validity.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
