Solving Radical Equations

Solve equations involving radicals (roots) or rational exponents by undoing (using inverse operations) and getting the x by itself. Extraneous solutions are explained and a number of examples are shown.

[davidtutorsmath]

Great question! This bugged me until I started teaching it. Though we answer the questions in the same manner (what squared is 25), they are 2 different questions. Think of the square root as a function. A function can only have 1 answer and so to evaluate sqrt(25) we answer 5 (what we call the principal square root, it will ALWAYS be positive). The other option is having an equation: x^2=25. There are two solutions to this equation (both + and - 5). One is a function and one an equation.

[anachanne]

Hello! My daughters and I have a question. On number 3, the problem ends up being the square root of 25, which you state must be positive 5. But we thought that when taking an even root, the solution could be either positive or negative. So why is it that stating the squre root of 25 = -5 makes the solution x = 24 invalid? Thanks!

[davidtutorsmath]

@imdabomb2635 Thanks! I wish all my students could be da bomb like you. :) Keep up the hard work.