Algebra 2: Solving Radical Equations

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Today we’re back with Algebra 2, this time solving for radical equations!  Did you say “Radical Equations?” As in wild and crazy equations? No, not exactly, radicals in math are used to take the square root, cubed root, or whatever root of a number.

Radicals are actually pretty cool because we can write them a couple of different ways and they all mean the same thing! Check it out below:Screen Shot 2020-05-12 at 11.23.20 AM.pngStill not sure of their coolness? Let’s see what they look like with actual numbers:
Screen Shot 2020-05-12 at 11.24.21 AM.pngExample: Solve the following algebraic equation below for the missing variable (aka, solve for x).Screen Shot 2020-05-12 at 11.25.03 AM.pngExplanation:

How do I answer this question?   

The question wants us to solve for x using our knowledge of radicals and algebra. You can also check out how to solve this question on Youtube here!

How do we do this? 

Step 1: We start solving this radical equation like any other algebraic problem: by getting x alone. We can do this easily by subtracting 7 and then dividing out 5.Screen Shot 2020-05-12 at 11.26.21 AM.pngStep 2: Now, to get rid of that pesky radical, we need to square the entire radical.  Remember, whatever we do to one side of the equation, we must also do to the other side of the equation, therefore, we also square 14 on the other side of the equal sign. 

*This gets rid of our radical and allows us to solve for x algebraically as normal!Screen Shot 2020-05-12 at 11.29.11 AM.pngScreen Shot 2020-05-12 at 11.29.34 AM.pngWhat happens when there is a cubed root though!?!? When dividing polynomials with different value roots, raise the entire radical to that same power of root to cancel it out:Screen Shot 2020-05-12 at 11.30.21 AM.pngRemember, we know radicals can also be written as fractions: Screen Shot 2020-05-12 at 11.31.01 AM.pngTherefore we also know that if we raise the entire radical expression to the same power of the root, the two exponents will cancel each other out:Screen Shot 2020-05-12 at 11.31.47 AM.pngWant more practice? Try solving these next few examples on your own. Screen Shot 2020-05-12 at 11.32.39 AM.pngWhen you’re ready, check out the below:Screen Shot 2020-05-12 at 11.33.12 AM.png

Did I miss anything?  Don’t let any questions go unchecked and let me know in the comments! Happy calculating! 🙂 

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Algebra 2: Dividing Polynomials

Screen Shot 2020-05-03 at 11.43.01 AMNow that everyone is home, there is no better time to go over dividing polynomials! Whether school is out or not, dividing polynomials will always come in handy… I think.

Either way at some point, you may need to know how to answer these types of questions. The cool thing about dividing polynomials is that it’s the same long division you did way back in grade school (except now with a lot of x). Ok, let’s get to it and check out the question below:

Also, if you haven’t done so, check out the video related that corresponds to this problem on Youtube! 🙂

Screen Shot 2020-05-04 at 10.21.17 PMExplanation:

How do I answer this question?

The question wants us to divide polynomials by using long division.

How do we do this?     

Step 1: First we set up a good ole’ division problem with the divisor, dividend, and quotient to solve.Screen Shot 2020-05-04 at 10.43.48 PM.pngStep 2: Now we use long division like we used to back in the day! If you have any confusion about this please check out the video in this post.Screen Shot 2020-05-04 at 10.22.52 PMScreen Shot 2020-05-04 at 10.23.27 PM.pngWhat happens when there is a remainder though!?!? When dividing polynomials with a remainder in the quotient, the answer is found and checked in a very similar way! Check it out below:
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Notice we represented the remainder by adding Screen Shot 2020-05-04 at 10.35.06 PM to our quotient! We just put the remainder over the divisor to represent this extra bit of solution.

Want more practice? Try solving these next few examples on your own. Screen Shot 2020-05-04 at 10.45.10 PM.pngWhen you’re ready, check out the solutions below:Screen Shot 2020-05-04 at 10.45.37 PMI hope everyone is finding something fun to do with all this extra time home! That can include everything from baking a cake to studying more math of course, happy calculating! 🙂 

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