SOLUTION: simplify 6 - 7 times the square root of 3 DIVIDED BY 2 times the square root of 3 + 4

Question 66033This question is from textbook an incremental development
: simplify
6 - 7 times the square root of 3
DIVIDED BY
2 times the square root of 3 + 4 This question is from textbook an incremental development

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
simplify
6 - 7 times the square root of 3
DIVIDED BY
2 times the square root of 3 + 4
(6-7sqrt3)/(4+2sqrt3)
First, multiply both numerator and denominator by(4-2sqrt3), the conjugate of (4+2sqrt3). This will get rid of the radical in the denominator.
NUMERATOR: (6-7sqrt3)(4-2sqrt3)=24-28sqrt3-12sqrt3+(14)(3)=66-40sqrt3
DENOMINATOR(4+2sqrt3)/(4-2sqrt3)=16+8sqrt3-8sqrt3-(4)(3)=16-12=4
Now we have
(66-40sqrt3)/4 divide numerator and denominator by 2 and we get:
(33-20sqrt3)/2
Hope this helps----ptaylor

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