Simplifying Nth Root Radicals (Integers or one variable)

Simplifying Nth Root Radicals

(Integers or one variable)

by Lloyd Thomas

​Fill this table out using only what you remember, no calculator.

​These are the squares I have memorized and find the most useful

​Complete this table if not completed

Put these to memory

​Parts of a Radical (Vocabulary)

​What do we call the "n"?

​Parts of a Radical (Vocabulary)

​What do we call the square root sign?

​Parts of a Radical (Vocabulary)

​What do we call the "a"?

​Parts of a Radical (Vocabulary)

​If we don't see an index number,

what is it assumed to be?

​Parts of a Radical (Vocabulary)

​Use a calculator and write your answer for each in the space given on your guided notes

​Be prepared to (probably) add to what your calculator gives you

Here are all of the roots (answers) for each radical. Notice some have 2 roots and others only 1 root.

​Even Index and Positive Radicand

​Odd Index and Positive Radicand

​Odd Index and Negative Radicand

​Even Index and Negative Radicand

​We can't have even roots of negative numbers, so your calculator gives you an error message if you try to find the even root of a negative number. But we can find an answer and they are imaginary numbers. We will get to it later.

​Time for the main event:

Simplifying Nth Root Radicals

​We will be finding groups of numbers under the radical to simplify Radicals

​

Why? Because of and

​

​Let's take first

​There are a pair of 2's and a pair of 5's inside the radical. Because the index number is 2, we take pairs of numbers out of the radical, and get the following.

​The index number is 3 so we are looking for groups of three numbers. There are a group of three 3's, so we can take all of the 3's out, leaving nothing under the radical.

​When simplifying radicals, what determines the group size of the same numbers we are looking for, in order to take them out of the radical?

​The index number

​Time to go to the example page you picked up on the way in.

​

​

​Then come back here for the procedure to simplify radicals and then a few practice problems. After all examples then you can do your homework.

​Simplifying Radicals:

​1) Break down radicand into its prime factors (factor tree)

​2) Rewrite all prime factors in numerical order under the radical.

​3) Find groups of the same #'s based on the index #.

​4)"Pull out" each group from the radical as only one of those numbers for each group, and keep all non-grouped #s in the radical

​5) All #s on the "outside" of the radical get multiplied together and All # on the "inside" of the radical get multiplied together.

​

​Let's go back to the guided notes for more examples, then come back here for a few practice problems, so I can see where you are as a class. Then you can work on your homework.

Multiple Choice

$$\sqrt{45}$$  =

• $$3\sqrt{5}$$  

• $$5\sqrt{3}$$  

• $$9\sqrt{5}$$  

• $$5\sqrt{9}$$  

Multiple Choice

$$\sqrt{147}$$  

• $$3\sqrt{49}$$  

• $$6\sqrt{3}$$  

• $$7\sqrt{3}$$  

• $$9\sqrt{7}$$  

Multiple Choice

$$\sqrt{112}$$  

• $$4\sqrt{7}$$  

• $$16\sqrt{3}$$  

• $$16\sqrt{7}$$  

• $$4\sqrt{3}$$  

​Assignments (Put in your planners)

​Due next class meeting

Recommended order of Completion:

​IXL: Roots of Integers; (100)

Delta Math: Simplify Basic Cube Roots;

​IXL: Simplify Radical Expressions; (100)

​IXL: Roots of Rational Numbers (Fractions) (100)