Algebra  sqrts
posted by John on .
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*640sqrt[12]+12sqrt[12]15*2
192  28sqrt[12] 30
162  28sqrt[12]
or am i missing a step?
19240sqrt[4*3]+12sqrt[4*3]30
16240*4sqrt[3]+12*4sqrt[3]
162160sqrt[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

first two ok
3.Multply
(8sqrt[6]+3sqrt[2])(4sqrt[6]5sqrt[2]
32sqrt[36]40sqrt[12]+12sqrt[12]15sqrt[4]
32*640sqrt[12]+12sqrt[12]15*2
192  28sqrt[12] 30
162  28sqrt[12] then
16228sqrt (4*3)
16228*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 (35)=2
I have no idea where you got this line in your work, it does not make sense
5sqrt[3]5sqrt[5]/ 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!