The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1
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WORKSHEET 7.2: MULTIPLYING RADICALS
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Multiplying radicals requires the use of the product property of square roots that states the
square root of a product equals the product of the square root of the factors.√xy=


x·√y,
wherexandyare real numbers that are greater than or equal to 0. Follow the steps below:


  1. Multiply the radicands.

  2. Simplify the radicals.

  3. Multiply the coefficients.


EXAMPLE
4


3 ·


6

4


3 ·


6 = 4


18

4


18 can be simplified as 4


9 ·


2.

4 · 3


2 = 12


2

DIRECTIONS: Simplify each expression.







4 ·


5 2.



7 ·


8 3. 3



6 · 2


3






15 ·


3 5. 2



5 ·


7 6. 3



3 ·


18


  1. − 4



3 ·


5 8. − 5



10 ·


8 9. − 3



10 · 4


15


  1. 6



8 ·


2 11. 3



10 ·


3 12. 8



2 ·− 2


2

CHALLENGE:Bobby said that he found a faster way to multiply radicals by
simplifying a radical before he multiplied. For example, when Bobby was
solving the problem


8 ·


6, he first expressed


8as2


2andthen
multiplied 2


2and


6, which equals 2



  1. Do you agree with his method?
    Will it always work? Explain.


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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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