This week in PreCalc 11 we learned how to solve radical equations (which is an equation where the variable is under a radical). It was easy if we used our basic knowledge of equations; what we do to one side we do to the other (if I added 25 to one side I would add 25 to the other side of the equal sign)  AND to cancel out an operation you do the opposite of it. (to cancel out -25 I would +25). With this basic knowledge it was pretty straight forward.

Example:

Explanation:

Step 1: apply the opposite operation to get rid of the square root

In the example, square roots were surrounding all the numbers in the equation so not much could be done without them gone. To get rid of the square roots you have to find the opposite operation which in this case will be to square everything. This is because once we square everything and it stays under the square root, the square root will cancel it out.

Step 2: bring like terms together

Now that the square root isn’t in the way of solving the equation we can do it now. First thing’s first, bring like terms together. The 5x and 2x are on opposite sides. So to remove the the 2x from the side it started on originally we have to subtract 2x to cancel it out. Then, since what we do on one side we do to the other, we have to add 2x to the other side. Now the -1 and 5 are on different sides of the equal sign so we have to +1 it started on originally and then +1 on the other side. After all the like terms are on the same side, combine them.

Step 3: SOLVE

All there really is to do is solve. To isolate x we have to divide by 3 and do that to the other side too. Then we are left with the answer which is 2.

Step 4:

Now that we know that x = 2 we need to verify our solution to make sure the root of the equation is a real root. For it to be a real root x has to be greater than or equal to 0. And once we have determined that, we have to put what x equals back into the original equation. In this case when I put 2 back into the original equation, both sides equal 3, therefore; 2 is a real root.