Algebra - sqrts

Square roots. Woohoo. Want to check some work I did.
1. Perform indicated operations
3sqrt[3]+2sqrt[27]-sqrt[12]
3sqrt[3]+2sqrt[3*9]-sqrt[2*6]
3sqrt[3]+3*2sqrt[3]-2sqrt[3]
3sqrt+6sqrt[3]-2sqrt[3]
= 7sqrt[3]

2.Simplify
sqrt[49x^12y^4z^8]
= 7x^6y^2z^4

3.Multply
(8sqrt[6]+3sqrt[2])(4sqrt[6]-5sqrt[2]
32sqrt[36]-40sqrt[12]+12sqrt[12]-15sqrt[4]
32*6-40sqrt[12]+12sqrt[12]-15*2
192 - 28sqrt[12] -30
162 - 28sqrt[12]

or am i missing a step?
192-40sqrt[4*3]+12sqrt[4*3]-30
162-40*4sqrt[3]+12*4sqrt[3]
162-160sqrt[3]+48sqrt[3]
162- 128sqrt[3] which I think turns into 162 -56sqrt[3]



1 last square root :
Rationalize the denominator
5/sqrt[3]+sqrt[5]=
5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]=
5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]=
5sqrt[3]-5sqrt[5]/-16 =
5sqrt[3]-5sqrt[5]/ -2

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  1. first two ok

    3.Multply
    (8sqrt[6]+3sqrt[2])(4sqrt[6]-5sqrt[2]
    32sqrt[36]-40sqrt[12]+12sqrt[12]-15sqrt[4]
    32*6-40sqrt[12]+12sqrt[12]-15*2
    192 - 28sqrt[12] -30
    162 - 28sqrt[12] then
    162-28sqrt (4*3)
    162-28*2sqrt3 and then multiply the 28*2


    1 last square root :
    Rationalize the denominator
    5/sqrt[3]+sqrt[5]=
    5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]=
    5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]=
    5sqrt[3]-5sqrt[5]/-16 = No. the demoniator is (3-5)=-2
    I have no idea where you got this line in your work, it does not make sense

    5sqrt[3]-5sqrt[5]/ -2

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    bobpursley
  2. Oh I see. So 1 more step on the first one and I had it.

    I see my big huge mistake on that last one. I went wild. I get it now.

    Thankyou!

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