DAY 2 – SIMPLIFYING RADICALS

& BASIC OPERATIONS

Simplify using only positive exponents

1.7n2 • 3n5 2. (4y6)3

Solve for the value of x3. 4.

WARM-UP #2 (10.7.2014)

6464 2042 yx

HOMEWORK CHECK

How can properties of exponents be used to write radical expressions in useful equivalent forms?

ESSENTIAL QUESTION #2 (10.7.2014)

We are familiar with taking square roots and even taking cubed roots, but you may not be as familiar with the elements of a radical.

WHAT IS A RADICAL?

An index in a radical tells you how many times you have to multiply the root times itself to get the radicand. When a radical is written without an index, there is an understood index of 2.

For example, in , 81 is the radicand, 9 is the root, and the index is 2. You have to multiply 9 by itself twice to get the radicand (9•9 = 92 = 81).

WHAT IS A RADICAL?

EVALUATING RADICALS

Radicand:Index:Root: because

Radicand:Index:Root: because

For some of the more complex problems, you can use a calculator to help

Step 1: Type in the indexStep 2: Press MATHStep 3: Choose 5Step 4: Type in the radicand

EVALUATING RADICALS WITH THE CALCULATOR

Now you will have a chance to practice some on your own. Complete the three examples on the bottom of the page. Then move to the next side and read the introduction carefully. Your goal is to come up with methods and shortcuts to simplify the radicals.

SIMPLIFYING RADICALS INVESTIGATION

1) Find the Prime Factorization of the radicand2) Any sets of “n” numbers (n=index) have one

representative multiplied outside3) Any remaining numbers not in a set are

multiplied inside.

SIMPLIFYING RADICALS

EXAMPLES

In your groups, complete the remaining problems

When written in radical form, it’s only possible to write two multiplied radicals as one if the index is the same.1) Multiply the coefficients2) Multiply the radicands3) Simplify!

MULTIPLYING RADICALS

EXAMPLES

In your groups, complete the remaining problems

You can only add or subtract radicals that contain the same index and radicand.

Just like you don’t change the variable expression, you won’t change the radical expression.

Only add and subtract the coefficients.

ALWAYS SIMPLFY THE RADICAL FIRST!

ADDING & SUBTRACTING RADICALS

EXAMPLES

In your groups, complete the remaining problems

“Lesson 2 - Simplifying Radicals Homework”

HOMEWORK: