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BELL-WORK Use your calculator to simplify (a) √2 •√2 (b) √5 •√5 Do you notice a pattern?

Square Property of Square Roots

CW 4.6 Review TB pg 616 # 17, 19, 25, 29

Materials Check

Due tomorow: PW 10-3 # 13-18(odd), 19-24 HW 4.4(c) Due tomorow: PW 10-3 # 13-18(odd), 19-24

HW 4.4(b) Solutions  

Guiding question: What is a simplified radical?

RECALL A simplified radical: Has no perfect square as its factor Has no radicals in the denominator We have discussed the multiplication property of square roots, now we will now discuss some other properties of square roots that will help us to simplify an expression that has a radical in the denominator.

Square Property of Square Roots 9

Square Property of Square Roots 3

Square Property of Square Roots 12

Division Property of Square Roots a ≥ 0, b > 0

Division Property of Square Roots Example:

Division Property of Square Roots Example:

Division Property of Square Roots Example:

Division Property of Square Roots Example: Is this a simplified radical?

Division Property of Square Roots Example: Is this a simplified radical? What can be done to get rid of the radical in the denominator?

Division Property of Square Roots Example:

Division Property of Square Roots Example:

Division Property of Square Roots Example: *This process is known as rationalizing the denominator.

Division Property of Square Roots Simplify:

Division Property of Square Roots Simplify:

Division Property of Square Roots Simplify:

Division Property of Square Roots Simplify:

Division Property of Square Roots Simplify:

Division Property of Square Roots Simplify:

Simplifying Radicals Multiply (√5 – √2)(√5 + √2) Does this type of multiplication problem look familiar? DOTS (a – b)(a + b) = a2 – b2 (√5 – √2)(√5 + √2) (√5)2 – (√2)2 5 – 2 3

Conjugate Property of Square Roots a ≥ 0, b ≥ 0

Conjugate Property of Square Roots Multiply (√6 – 3√21)(√6 + 3√21) (√6)2 – (3√21)2 6 – 9•21 -183 (√7 – 4√13)(√7 + 4√13) (√7)2 – (4√13)2 7 – 16•13 -201

Simplifying Radicals Simplify:

Simplifying Radicals Simplify: What can be done to get rid of the radicals in the denominator?

Simplifying Radicals Simplify:

Simplifying Radicals Simplify: = 8√7 + 8√3 7 – 3

Simplifying Radicals Simplify: = 8√7 + 8√3 7 – 3 4

Simplifying Radicals Simplify: = 8√7 + 8√3 7 – 3 4 = 2√7 + 2√3

Rationalizing the Denominator To simplify an expression with a radical in the denominator multiply by the radical. To simplify an expression with a sum or difference of radicals in the denominator, multiply by the conjugate of the denominator.

Simplifying Radicals Simplify:

Simplifying Radicals Simplify:

Simplifying Radicals Simplify: = 9√12 – 9√11 12 – 11

Simplifying Radicals Simplify: = 9√12 – 9√11 12 – 11

Simplifying Radicals Simplify: = 9√12 – 9√11 12 – 11 = 18√3 – 9√11

Simplifying Radicals Complete TB pg 616 # 30,31,33

Who wants to answer the Guiding question? What is a simplified radical?

CW 4.7 Detach a sheet of notebook paper from the CW section of your notebook. Complete: TB pg 616 # 9,15,21,28,29