- Monday: 6-5 Equations Containing Radicals:
On Monday we looked over the blog from last week and went over some of the problems that occurred in our homework on Equations Containing Radicals.
As the name would suggest, these are equations that contain a square root. The first step in solving on of these equations is to isolate the square root or radical...
As the name would suggest, these are equations that contain a square root. The first step in solving on of these equations is to isolate the square root or radical...
...with the radical isolated, one squares both sides of the equation...
...and set the equation equal to zero...
The next step is to factor the equation and find the value of x...
The final step in solving an equation of this nature is the ever important step of checking the solutions by plugging them back into the original equation...
Tips:
-Don't forget to check the solutions or you might end up with a solution that doesn't work.
-Be sure to square the whole root and not individual terms as this may lead to an incorrect solution.
-When you have two square roots, it is important to get the roots on different sides or the equal sign.
Here is a video that illustrates how to solve an equation this two roots.
This material is covered in pages 263-266 of the text book and problems from this section appear in self test 1 on page 267 as well in the chapter review and Chapter test on pages 286-287.
-Tuesday: Overview of Section Six:
On Tuesday we reviewed our homework which covered the material from section 6 that we have learned so far.
Some common mistakes that we went over evolved the properties of radicals and the use of conjugates.
-Properties of Radicals:
Here is one of the problems were went over that concerns this subject...
The first thing to do in solving this type of problem is to multiply it by a term that will that will make the denominator a perfect square, cube, ect...
On Tuesday we reviewed our homework which covered the material from section 6 that we have learned so far.
Some common mistakes that we went over evolved the properties of radicals and the use of conjugates.
-Properties of Radicals:
Here is one of the problems were went over that concerns this subject...
With the denominator cleaned up and a square root remaining on the top, solving the rest of the problem is fairly simple...
-Conjugates:
When one is faced with a problem with two roots in the denominator, it is necessary to us the conjugate of the denominator. The conjugate is the same as the original equation except the sign is the opposite. For example, the conjugate of 3x-6y would be 3x+6y.
Here is an equation evolving conjugates that we worked on today:
The first step is to multiple by the conjugate...
When one is faced with a problem with two roots in the denominator, it is necessary to us the conjugate of the denominator. The conjugate is the same as the original equation except the sign is the opposite. For example, the conjugate of 3x-6y would be 3x+6y.
Here is an equation evolving conjugates that we worked on today:
At this point, the bottom works out to 8 which cancels with the numbers in the top...
Leaving us with...
Tips:
-Remember, the conjugate is the same as the original equation only the sign is different.
Example: The conjugate of 3x-6y would be 3x+6y
-To clean up the bottom in a fraction with roots in the numerator and the denominator, multiply the whole equation by something that will make the bottom a perfect square, cube, ect.
In the text book, section six spans from page 248-289 and covers irrational and complex numbers.
Applications:
-Irrational numbers such as pi are used to find the circumference of a circle
-Irrational numbers are always more exact the physical measurements
In the text book, section six spans from page 248-289 and covers irrational and complex numbers.
Applications:
-Irrational numbers such as pi are used to find the circumference of a circle
-Irrational numbers are always more exact the physical measurements
Great work Cooper. I loved how you incorporated the directions to solving the equations within the actual problems because it makes for very easy understanding. The tips and applications sections were very informative and useful. When you say to multiply by the conjugate, it might be helpful to explain what that actually is in case someone forgot, but the rest of the post was perfect.
ReplyDeleteNice post Cooper, I liked how you started the blog with a reminder of how to take care of radicals in equations. It was easy to follow and nicely done. The tips section is a helpful tool to not have careless mistakes happen and to just make things easier in certain circumstances. The video was also a good example of a problem with radicals being done step by step which really broke things down and made everything clear. The next section was also very organized and it gave a good reminder how to use conjugates in the right places.
ReplyDeleteThis blog was really well organized and easy to follow. I like how you gave us tips and lots of examples. It was nice how you wrote out each step to, and explained it instead of just writing the problem. Good job!
ReplyDeleteHello! Sorry this is a little late, but this was a great blog. It really helped me review for the test with the example problems and the way that it was very easy to follow because of the organization. Thins that I thought were very helpful is having the problems written out an the tips section! Great post!
ReplyDeleteGreat blog! You presented the example problems really clearly by writing them out, which was really helpful. I liked that you added tips to remember and how you explained what you were doing. I also found it helpful that you addressed a common mistake made in class with these problems. This blog is going to be useful to study with for exams!
ReplyDelete