**Module 8**

Module 8 was about...

Section 1

In section 1 we learned how to simplify radical expressions. We did roots of a radical. we simplified them and if we found two numbers that matched, we would move to the outside of the radical sign

Section 2

Section 3

In section 3 we learned about rationalization. You're not allowed to have a rational expression in the denominator so you have to rationalize it.

-Simplifying radical expressions

-Finding the Domain of radical expressions

-Rationalization

-Radicals

-Complex numbers

A common mistake is for a person is to forget to combine two radical expressions, then simplifying

In section 2, we learned how to find the domain of radical expressions and we learned how to solve operations with radicals. To find the the restricted domain, you set the denominator equal to 0, find the excluded values and put the excluded values in parenthetical ciation, which is the restricted domain.

For operations with radicals you find common radicals and then add or subtract the number in front of the radical.

Common mistakes are forgetting to find common radicals and trying to add or subtract uncommon radicals √12 +√3

Knowing how to solve radicals is necessary for many computer science professions

A common mistake is for a person to forget is to rationalize both the numerator and the denominator

Section 4: Rational exponents

Rational exponents can be written as fraction as well as not a fraction. If the exponent is negative you put everything over 1. Always remember to rationalize answers. When you are raising a power to a power you multiply you add or subtract in all other cases.

Common mistakes are forgetting to rationalize and not following algebraic rules. Scientists in many different fields need to know how to do this.

Section 5

In section 5 we learned how to solve radical eqations by isolating the radical. This helps you know how to solve equations with radicals in it for future sections.

A common mistake is to forget to search for a extraneous root in the solution.

Section 6:Roots and X-intercepst

X-intercepts are spots where y=0. You find x-intercepts by factoring the equation, simplifying it and setting it equal to zero. The roots are usually going to be the same as the x- intercepts. If their is only one x- intercept then that is the vertex as well. If the vertex is above the x axis an palabara goes up their will not be x- intercepts and the roots will be complex.

Engineers use this often. Mistakes could come when someone would not know what to do when equation is non factorable.

Section 7

In section 7 we learned how to find the conjugate of complex numbers. This helps solve more complex numbers when they are added or multiplied together.

A common mistake is to forget that the conjugate applies to conplex numbers or imaginary numbers.

Section 8: Complex numbers and equations

These types of equations will sometimes have i's in them. What you want to do to solve these is bring all the x's to one side and then solve. You might need to distribute but might not need to. Always remember to rationalize answers.

A common mistake is not knowing when and when not to distribute. Aerospace and nuclear engineers use this.