Expert: Richard J. Raridon - 4/29/2009

Question
Could you please tell me and tell me if these are correct Thank-you!

1. Simplify
   Root:3 (-512x)^3       Answer -8x

2. Use rational exponents to simplify.
Sqrt(x^4y^10)                Answer  x^2y^5

3. Simplify by factoring.
    Sqrt (500x^4)            Answer 10x^2sqrt5

4.   Simplify by factoring.
Root:4 (162)       Answer 36sqrt2
    Simplify by factoring. Assume that all expressions under the radical represent nonnegative numbers.
5.  Root:5 (288x^17y^10)       Answer  60x^8y^5sqrt2x
6.  Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
    sqrt(5b^5)sqrt(15c^6)           Answer 5b^2c^3sqrt36

7. Divide. Then simplify by taking roots, if possible. Assume that all expressions under radicals represent positive numbers.
     sqrt(35a)/sqrt(5a)      Answer sqrt7

8. root:5(32x^11)/(y^20       Not sure of this one


9. Add or subtract. Simplify by collecting like radical terms, if possible.
   6sqrt(2)-2sqrt(2)+7sqrt(2)         Answer 11sqrt2

10. Add. Simplify by collecting like radical terms if possible.
    4sqrt(108)+2sqrt(27)        Answer 30sqrt3

11. Add. Simplify by collection like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers.
      sqrt(7a)+5sqrt(63a^3)        Answer sqrt7a+15a sqrt7a
      
12. Root:3(a) (root:3(2a^2) +root:3(16a^2)          Not sure of this one


Answer
1. (-512x^3)^1/3 = -8x
2. ok
3. you can write it 10x^2(5)^1/2
4. (162)^1/2 = 9(2)^1/2
5. (288x^17y^10)^1/2 = 12x^8y^5(2x)^1/2
6. 5b^2c^3(3)^1/2
7. you can write it 7^1/2
8. 4x^5(2x)^1/2/y^10
9. you can write it 11(2)^1/2
10. you can write it 30(3)^1/2
11. you can write it (15a+1)(7a)^1/2
12. (2a^2)^1/3 +(16a^2)^1/3 = 3(2a^2)^1/3