Algebra II: Chapter 5 Part 2 (5-5:5-9) Operations with Polynomials

5.5: Roots of Real Numbers

Finding the _________________________ of a number and _________________________ a number are

inverse operations. To find the __________________________ of a number �, you must find a number whose

square is �.

Since finding the square root of a number and squaring a number are inverse operations. It makes sense that the

inverse of raising a number to the ��� power is finding the ______________________ of a number.

The symbol √50�

indicates the __________________ of 50.

√50�

Some numbers have more than ___________ real ��� root. For example, 36 has two square

roots ____ and ____. When there is more than one real root, the nonnegative root is called the

____________________________. When no index is given, as in √36, the radical sign indicates the

______________________________________________.

When you find the ��� root of an even power and the result is an odd power, you must take the

_____________________________________________________ of the result to ensure that the answer is

nonnegative.

HW:

Algebra II: Chapter 5 Part 2 (5-5:5-9) Operations with Polynomials

5.6: Radical Expressions Part 1

Follow these steps to simplify a square root.

1) Factor the ________________________ into as many ___________________ as possible.

2) Use the Product Property to isolate the ________________________________________.

3) _______________________ each radical.

To eliminate radicals from a denominator, use a process called ______________________________________.

HW:

5.6: Radical Expressions Part 2

You CANNOT _____________________ radicals in the same manner that you multiply or divide radicals.

You add/subtract radicals in the same manner that you add/subtract ______________________________.

Two radical expressions are like radical expressions if they meet two requirements:

1) ____________________________________________________________

2) ____________________________________________________________

Binomials of the form ________________________________________, such as in Examples 5a and 5b, are

called ____________________________________________. The product of conjugates is always a

________________________ number. We can use conjugates to ____________________________ a

denominator.

HW:

Algebra II: Chapter 5 Part 2 (5-5:5-9) Operations with Polynomials

5.7: Rational Exponents

This example suggests a rule: ��

�= ___________________.

HW:

Algebra II: Chapter 5 Part 2 (5-5:5-9) Operations with Polynomials

5.8: Solving Radical Equations

Equations with radicals that have variables in the radicands are called _________________________________.

To solve this type of equations, __________________ each side of the equation to a power equal to the index of

the __________________________________.

*** When solving radical equations, it is VERY important to ___________________ your answers. If the

answer does not work, it is called an ________________________________.

HW:

Algebra II: Chapter 5 Part 2 (5-5:5-9) Operations with Polynomials

5.9: Complex Numbers Part 1

Solve: �� � 1 � 0

This equation has ___________ real solutions. French Mathematician Rene Descartes proposed that a number

_____ be defined such that ______________________.

Adding and Subtracting Complex Numbers: i is called the ______________________________________.

Numbers of the form �, 2�, and �√2 are called ________________________________________________.

A number with a real component and an imaginary component is called a _____________________ number.

HW: Part 1

5.9 Part 2

Use the FOIL method to __________________________ complex numbers.

Two complex numbers of the form ______________ and ________________ are called complex

_______________________________. We use complex conjugates to simplify quotients of complex numbers.

HW: Part Two