Nth Roots and Simplifying Radicals

Simplifying Radicals

(Integers or one variable)

​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

Fill in the Blank

Parts of a Radical Vocabulary

$$\sqrt[n]{x^a}$$

What do we call the "n"?

Fill in the Blank

$$\sqrt[n]{x^a}$$

What do we call the "x"?

Fill in the Blank

$$\sqrt[n]{x^a}$$

What do we call the "a"?

Fill in the Blank

$$\sqrt[n]{x^a}$$

What do we call the root symbol?

Math Response

Use a calculator to find the correct answer (if answer has 2 roots separate with parenthesis):

$$\sqrt[]{289}=$$

Type answer here

Correct Answer: \left(17\right)\left(-17\right)

Deg^°

Rad

Math Response

Use a calculator to find the correct answer (if answer has 2 roots separate with parenthesis):

$$\sqrt[3]{343}=$$

Type answer here

Correct Answer: 7

Deg^°

Rad

Math Response

Use a calculator to find the correct answer (if answer has 2 roots separate with parenthesis):

$$\sqrt[3]{-125}=$$

Type answer here

Correct Answer: -5

Deg^°

Rad

Math Response

Use a calculator to find the correct answer (if answer has 2 roots separate with parenthesis):

$$\sqrt[4]{2401}=$$

Type answer here

Correct Answer: \left(7\right)\left(-7\right)

Deg^°

Rad

Drag and Drop

If the index is even and the radicand is positive there will be ​

Placeholder

​

Placeholder

root(s).

Drag these tiles and drop them in the correct blank above

two

real

one

three

imaginary

Drag and Drop

If the index is even and the radicand is negative there will be ​

Placeholder

​

Placeholder

root(s).

Drag these tiles and drop them in the correct blank above

two

real

one

three

imaginary

Drag and Drop

If the index is even and the radicand is positive there will be ​

Placeholder

​

Placeholder

root(s).

Drag these tiles and drop them in the correct blank above

two

real

one

three

imaginary

Drag and Drop

If the index is odd and the radicand is negative there will be ​

Placeholder

​

Placeholder

root(s).

Drag these tiles and drop them in the correct blank above

two

real

one

three

imaginary

​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.

Fill in the Blank

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?

​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.

​

​

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

$$\sqrt{112}$$  

• $$4\sqrt{7}$$  

• $$16\sqrt{3}$$  

• $$16\sqrt{7}$$  

• $$4\sqrt{3}$$  

​Assignment:

​Due next class meeting

Google Classroom - Simplify Radicals Review
Google Classroom - Add, Subtract, & Multiply Radical Expressions