Warm Up - Copy the following vocabulary words 1. 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?

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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 ⅓ 3.√2 4.-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 number 2.For every pair of factors take 1 out 3.Multiply the factors on the outside together and the factors on the inside together

Example 1 Simplify √12 Step 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 √16x 4

Let’s try one more √216 x 5 y 7