How You Can (And Should) Get More Practice!

Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.

Theoretically Easier Difficulty Problem

Start by squaring both sides.
Solve for as normal.
Remember to check your solutions to see if they work - it is possible to do everything correct, and still get a bad answer - known as an “extraneous solution”.

What is the real-valued solutions to the following equality? (If there is no answer, enter DNE). .

Theoretically Medium Difficulty Problem

Start by squaring both sides.
Solve for as normal.
It’s possible the resulting function, once you have gotten rid of the radicals, may not be solveable; in which case the answer is: DNE.
Remember to check your answers; it’s possible you did nothing wrong in the computation and still get a number that doesn’t work. These are the ’extraneous solutions’

What is the sum of the real-valued solutions to the following equality? (If there are no solutions, enter DNE) .

Theoretically Harder Difficulty Problem

Start by isolating one of the square roots and then squaring both sides.
Remember to expand out both sides correctly. For the side you isolated a square root, squaring that side should simply remove the square root. For the other side, you may need to expand out the square by using distribution.
Once you have expanded out everything, isolate the remaining square root (if there is one) and square both sides again to get rid of the last square root.
Once no more square roots remain, solve for as normal.
Remember to check your solutions to see if they work - it is possible to do everything correct, and still get a bad answer - known as an “extraneous solution”.

What is the sum of the real-valued solutions to the following equality? If there are no solutions, enter DNE) The sum of solutions is: .