Warm Up - Copy the following vocabulary words1. Index: The number outside the radical symbol.

2. Radicand: is the number found inside a radical symbol, and it is the number you want to find the root of

3. Radical: An expression that uses a root, such as square root, cube root.

Essential Question:

How can I simplify square roots?

Gallery

Did Analytic Geometry Home work

False, I wrote the problem down and called it a night

Standard(s):

Rewrite expressions involving radicals(i.e.,simplify and/or use the operations of addition, subtraction,and multiplication, with radicals within expressions limited to square roots).

Unit 4: Extending the number system

Section 1: Rewriting radical expressions

Let’s talk about the number system

Real number : the set of all numbers that can be expressed as a decimal or that are on the number line. Real numbers have certain properties and different classifications, including natural, whole, integers, rational and irrational.

Irrational number- real numbers that cannot be represented as terminating or repeating decimals. Example ∏, e, √2

Rational number: A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers.

Natural numbers: 1,2,3,4,...

Whole numbers. The numbers 0, 1, 2, 3, …. Integers: …,-3,-2,-1,0,1,2,3,…

Classify the Following numbers using your chart 1.32.⅓ 3.√24.-3

The language of radicals

Identify the index and the radicand

When the index is 2 you don’t have to write it

Simplifying square roots When you have a square root the index is 2. Steps to simplifying a square root:1.Make a factor tree and break down

the number2.For every pair of factors take 1 out3.Multiply the factors on the outside

together and the factors on the inside together

Example 1Simplify √12Step 1: make a factor tree

Example continued

Step 2: For every pair of factors take one out

Example continued

Step 3: Multiply the factors on the outside together, then multiply the factors on the inside together

Example 2:

√36

Try these in your notes

√96

√18

√98

What if we add variables

√16x4

Let’s try one more

√216 x5y7