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Unit 3 Summary Assignment – Pre Calc 11 – Adam Merbah

For the Unit 3 summary assignment, we were assigned the task of demonstrating a mathematical concept presented to us throughout the past week. For this assignment, I chose to demonstrate how to solve quadratics with radicals (3.3)

Solving Quadtratics with Radicals

Let’s say you have a quadratic equation that is unsimplified. The first thing you would usually want to do is to turn it into Ax2 =-+ bx + = 0 ( general form). But what if you have a Radical expression mixed into the equation? leaving the radical sign intact would not work with quadratics, so the first step is to square everything under the radical sign to get rid of the radical sign. In return, we would have to square everything on the other side of the equation as well. After that, your values should be ready to simplify and to be turned into Ax2 + Bx + C = 0 form. With the Ax2 + Bx + c Form, you can then go ahead and factor and solve your equation to find your x values.

Important Note: When dealing with radicals, ALWAYS check both your solutions as one of them could not work!

Ex 1 :

 

When dealing with coefficients, leave them as they are and make sure to use them while factoring.

Ex 2 :

 

Unit 2 Summary Assignment – Pre calc 11 – Adam Merbah

For the Unit 2 summary assignment, were assigned the task of demonstrating a mathematical concept learned throughout the past week. For this post, I chose to demonstrate my understanding of dividing Radical expressions.

Dividing Radical Expressions

Let’s say you have a number divided by radical. The first thing you want to do is take the radicand at the denominator section of the fraction and use that to rationalize your denominator. The way you would Rationalize it is by multiplying both the denominator and numerator by what’s at the bottom of the fraction (denominator/ radicand).  make sure to not multiply with the coefficient next to radicand, as we are only using the radicand to rationalize in this case. Afterwards, you want to evaluate the fraction by multiplying your values correctly, reducing numbers that can be reduced, and then simplifying the radicand if it’s a perfect square.

Ex :  

Note: Multiplying a fraction by 1 will not change its value

 

Dividing Radical Expression with BINOMIALS

When the radical denominator is a binomial, we use the conjugate to rationalize the denominator.

What’s the Conjugate? : The conjugate can mean the opposite of the given expression. for example, The conjugate of 2x+3 would be 2x-3. Make sure you know that the conjugates will always     cancel each other out.

Unlike the example in the first explanation, instead of only using the radicand to rationalize fraction, we take the entire expression at the denominator spot and use the conjugate of the expression to rationalize the entire fraction. If you see conjugates at the denominator, you can simply cancel them out. Multiply the Denominator and numerator and simplify as much as possible.

ex :