SOLUTION: Hey I a having troubles rationalizing the denominator and simplifying equations. I hope you guys can help me! It would be great if you show the steps so I could understand. (

Algebra ->  Radicals -> SOLUTION: Hey I a having troubles rationalizing the denominator and simplifying equations. I hope you guys can help me! It would be great if you show the steps so I could understand. (      Log On


   

Question 886714: Hey I a having troubles rationalizing the denominator and simplifying equations.
I hope you guys can help me! It would be great if you show the steps so I could understand.

(3√5-7√10)/√6

3√120/√108


√30+3√3/√30-3√3

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is for the second expression in the list:

√30+3√3/√30-3√3
For rendering on the page, that is sqrt(30)+3sqrt(3)/sqrt(30)-3sqrt(30)
sqrt%2830%29%2B3sqrt%283%29%2Fsqrt%2830%29-3sqrt%2830%29



sqrt%2830%29%2B3%2Asqrt%283%29sqrt%2830%29%2F30-3sqrt%2830%29

sqrt%2830%29%2Bsqrt%2890%29%2F10-3sqrt%2830%29

sqrt%289%2A10%29%2F10-2sqrt%2830%29

highlight%283sqrt%2810%29%2F10-2sqrt%2830%29%29
or
highlight%28%283sqrt%2830%29-20sqrt%2830%29%29%2F10%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Hey I a having troubles rationalizing the denominator and simplifying equations.
I hope you guys can help me! It would be great if you show the steps so I could understand.
(3√5-7√10)/√6
3√120/√108
√30+3√3/√30-3√3


%283sqrt%285%29+-+7sqrt%2810%29%29%2Fsqrt%286%29______%28sqrt%286%29%283sqrt%285%29+-+7sqrt%2810%29%29%29%2Fsqrt%286%29sqrt%286%29_______%283sqrt%2830%29+-+7sqrt%2860%29%29%2F6

%283sqrt%2830%29+-+7sqrt%282%5E2+%2A+15%29%29%2F6________%283sqrt%2830%29+-+14sqrt%2815%29%29%2F6, or sqrt%2830%29%2F2+-+7sqrt%2815%29%2F3



3sqrt%28120%29%2Fsqrt%28108%29_______3sqrt%28120%2F108%29

3sqrt%2810%2F9%29 ----- Reducing radicand 

3sqrt%2810%29%2Fsqrt%289%29

%283sqrt%2810%29sqrt%289%29%29%2Fsqrt%289%29sqrt%289%29 ------ Rationalizing denominator

3sqrt%2890%29%2F9_______3sqrt%283%5E2+%2A+10%29%2F9_______9sqrt%2810%29%2F9______cross%289%29sqrt%2810%29%2Fcross%289%29______highlight_green%28highlight_green%28sqrt%2810%29%29%29



Is the 3rd: sqrt%2830%29+%2B+3sqrt%283%29%2Fsqrt%2830%29+-+3sqrt%283%29?