Questions on Algebra: Square root, cubic root, N-th root answered by real tutors!

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Question 151258: Expand and simplify the following: (sqrt4 + sqrt3)(sqrt2 - sqrt4)
*This is the same equation I have sent previously, however, I wanted to add more information for you to understand.
: Expand and simplify the following: (sqrt4 + sqrt3)(sqrt2 - sqrt4)
*This is the same equation I have sent previously, however, I wanted to add more information for you to understand.

Answer by joLeeBee(6) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt4 + sqrt3)(sqrt2 + sqrt4)
-> sqrt4*sqrt2 - sqrt4^2 + sqrt3*sqrt2 - sqrt3*sqrt4
2*sqrt2 + sqrt3*sqrt2 - sqrt3*2 - 4
2^1*2^1/2 + sqrt6 - 2sqrt3 -4
2^3/2 + sqrt6 - 2sqrt3 - 4
-->cuberoot4 + sqrt6 - 2sqrt3 - 4
Question 151258: Expand and simplify the following: (sqrt4 + sqrt3)(sqrt2 - sqrt4)
*This is the same equation I have sent previously, however, I wanted to add more information for you to understand.
: Expand and simplify the following: (sqrt4 + sqrt3)(sqrt2 - sqrt4)
*This is the same equation I have sent previously, however, I wanted to add more information for you to understand.

Answer by jim_thompson5910(9217) About Me  (Show Source):
You can put this solution on YOUR website!

(sqrt(4)+sqrt(3))(sqrt(2)-sqrt(4)) Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


(highlight(sqrt(4))+sqrt(3))(highlight(sqrt(2))-sqrt(4)) Multiply the First terms:(sqrt(4))*(sqrt(2))=sqrt(8)=2*sqrt(2).


(highlight(sqrt(4))+sqrt(3))(sqrt(2)+highlight(-sqrt(4))) Multiply the Outer terms:(sqrt(4))*(-sqrt(4))=-4.


(sqrt(4)+highlight(sqrt(3)))(highlight(sqrt(2))-sqrt(4)) Multiply the Inner terms:(sqrt(3))*(sqrt(2))=sqrt(6).


(sqrt(4)+highlight(sqrt(3)))(sqrt(2)+highlight(-sqrt(4))) Multiply the Last terms:(sqrt(3))*(-sqrt(4))=-sqrt(12)=-2*sqrt(3).


2*sqrt(2)-4+sqrt(6)-2*sqrt(3) Now collect every term to make a single expression.


So (sqrt(4)+sqrt(3))(sqrt(2)-sqrt(4)) FOILs to 2*sqrt(2)-4+sqrt(6)-2*sqrt(3).


In other words, (sqrt(4)+sqrt(3))(sqrt(2)-sqrt(4))=2*sqrt(2)-4+sqrt(6)-2*sqrt(3).