Mr.Talent, Mrs.Young & Mrs.Reynolds Aim: How do we simplify radicals? Simplify radicals with numerical indexes of 2 or more 1. Find the GCF

2. Make sure one is the

greatest perfect square.

3. Find the square root of it.

4. Place the rational number in

front of the radical

Students will be able to

1. Simplify radicals with numerical indexes of 2 or more

2. Simplify radicals involving monomial radicands

3. Explain the procedure for simplifying radical expressions

4. Explain how to determine when a radical is in simplest form Radicals- the square root sign

Radicands-the number in/under the sign Using Prior

Knowledge Whenever you have an index that number represents how many times the root needs to be multiplied by itself to equal the radicand.

*When there is no index and its just the radical sign( ) then the index will always be 2.

Example #1.

3 8

Your root/answer has to multiply by itself 3 times(index) to get 8(radicand)

What will be your answer? Simplifying Radicals Index- number or variable given as a superscript before a square-root sign showing which root is to be taken. Terms-to-know: by Simplify the radical/

find the square root

1.√ 121

2.√ 400

3. √256 Do Now 64 1000 4. 256 81 You Try: Part. 4 Part 1 27 Index Radicand Radical Explain how to determine

when a radical is in simplest form You know when a radical is in simplest form when the radicand is prime and cant be broken down further. 1. 2. 3. Part 2 Explain the procedure for simplifying radical expressions Example:

80 16 5 4 5 Part 3 Simplify radicals involving monomial radicands You try: 45 125 28 Step 1:Factor the radicand to isolate the perfect power factor(s).

*the perfect power factors would be 8 x y notice in isolation the index travels with both.

Step 2:Simplify the perfect power(square roots in this case only because there is no indicated index) factor(s).

Step 3: combine the simplified radicand(2xy) with the factored out radicand ( 6y ) 24x y 4x y 6y 2xy 6y Your just bringing down this factored radicand and combining it with the simplified radicand 3 2 2 2 2 2 In this step the "y" becomes y because it the exponent 3 factored out by 6y 2 example: 81x y 7 10 27x 3 * x y 3 y y * * * 3 3 3 3xy 3x y 2 3 3xy You try: 32x y 13 13 54x y 9 8 256x y 20 31 NYS standards: A2.A13

C.C. standards : Exit Question: What determines the perfect power in which the radicand is factored by?

*when dealing with simplification of radicals "Root" is just another way to say answer

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# Simplifying Radicals

Trigonometry Lesson Plan Project

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