College Algebra

I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps.

Rationalize each expression by building perfect nth root factors for each denominator. Assume all variables represent positive quantities.

1. 3/Square root 12

2. Square root 27/50 b The square root on this problem covers the whole problems.

3. -4/square root 20

4. square root 125/12n^3 The square root on this question covers the whole problem.

Simplify the following expressions by rationalizing the denominators were possible, state results in exact from and approximate form, rounded to hundredths.

5. 8/3 + square root 11

6. 6/square root x - square root 2

7. 7/ square root 7 + 3

8. Square root 10 - 3 / square root 3 + square root 2

9. 7 + square root 6/ 3-3 square root 2

Thanks for your help my professor is not at all helpful and the book that is provided only explains basic examples rather then some like what we have to work through.

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  1. I will do #4 and #8 ,you try the rest and let me know where you run into problems

    #4

    -4/√20
    = -4/(2√5) = -2/√5
    = -2/√5 * √5/√5
    = -2√5/5 , now check with your calculator to see if correct

    #8

    (√10 - 3)/(√3 + √2)
    = (√10 - 3)/(√3 + √2) * (√3 - √2)/(√3 - √2)
    = (√30 - √20 -3√3 - 3√2)/(3-2)
    = √30 - 2√5 - 3√3 + 3√2

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