Sponge What operation does each term represent? Create an example for each. 1. Sum 2. Difference 3. Twice 4. Decreased 5. Together 6. Square

Radical Sign (square root sign) Radicand Numbers or variables under the radical sign

Prime Numbers What type of numbers are these? 2 3 5 7 11 13…

Perfect Squares Copy! 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

Simplify = 2 = 4 = 5 This is a piece of cake! = 10 = 12

Radicals are in SIMPLEST FORM when.. 1. No perfect square factors other than 1 are under the radical. No fractions are under the radical. No radicals are in the denominator.

Let’s review! Factor Trees to Prime Factorization 45

Let’s review! Factor Trees to Prime Factorization 54

When you have a pair, bring the number out. EX:1 Simplify. When you have a pair, bring the number out.

EX:3

When you have a pair, bring the number out. EX:2 Simplify When you have a pair, bring the number out.

EX:4 Simplify.

You try! 1. 2. 3. 4.

Sponge

= Simplify = = = = = = = = = Perfect Square Factor * Other Factor Get Ready! = Simplify = = = LEAVE IN RADICAL FORM = = = = = =

Examples with variables:

Examples:

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

+ To combine radicals: combine the coefficients of like radicals Combining Radicals + To combine radicals: combine the coefficients of like radicals

Simplify each expression

Simplify each expression: Simplify each radical first and then combine.

Simplify each expression: Simplify each radical first and then combine.

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

Simplify each expression

Simplify each expression

Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

Multiply and then simplify

Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

That was easy!

42 cannot be simplified, so we are finished. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

This can be divided which leaves the radical in the denominator This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

This cannot be divided which leaves the radical in the denominator This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. Reduce the fraction.

Simplify = X = Y3 = P2X3Y = 2X2Y = 5C4D10

Simplify = = = =

= = ? = =