Multiplication and Division of Radicals

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For each of the following questions, assume all variables are nonnegative real numbers.

1. Multiply sqrt(8) * sqrt(2).


  -4

  4

 sqrt(16)


2. Multiply sqrt(6) * sqrt(5).

  2*sqrt(15)

  sqrt(30)

  sqrt(11)


3. Multiply 2aqrt(3) * 3sqrt(5).

  75

  5*sqrt(15)

  6*sqrt(15)


4. Multiply (sqrt(x) - 1) * (sqrt(x) + 1).

 sqrt(x^2) - 1

 x + 1

 x - 1



5. Multiply (6*cuberoot(x)) * (2*cuberoot(x^5)).

 12* cuberoot(x^6)
 12* ninthroot(x^6)

 12x2


6. Multiply (x - sqrt(7))^2.


 x^2 - 2sqrt(7) + 7

  x^2 - 2sqrt(7) + 49

  x - 2sqrt(7) + 7


7. Rationalize the denominator of sqrt(3) / [(sqrt(5) - sqrt(2)].


 1

  [sqrt(15) sqrt(6)/3

 [sqrt(15) + sqrt(6)/3]


8. Rationalize the denominator of [sqrt(x) - sqrt(y)] / [sqrt(x) + sqrt(y)].


 [x - 2sqrt(xy) + y] / [x-y]

  [x + 2sqrt(xy) - y] / [x+y]

  -1



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Copyright © 2001 Donna Tupper.