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 Simplify`sqrt(18)/(sqrt(8)-3)` , `(4-3sqrt(2))^2`  and `*sqrt(5b ^2d)`    

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novjb | (Level 1) Salutatorian

Posted May 23, 2013 at 9:40 PM via web

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 Simplify`sqrt(18)/(sqrt(8)-3)` , `(4-3sqrt(2))^2`  and `*sqrt(5b ^2d)`

 

 

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ishpiro | Teacher | (Level 2) Associate Educator

Posted May 23, 2013 at 11:03 PM (Answer #1)

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`sqrt(18)/(sqrt(8) - 3) = sqrt(2*9)/(sqrt(2*4) - 3) = (3sqrt(2))/(2sqrt(2)-3) `

Rationalize the denominator by multiplying both numerator and denominator by `2sqrt(2) + 3` :

`(3sqrt(2) * (2sqrt(2) + 3))/((2sqrt(2) -3)(2sqrt(2) + 3)) = (3*2*2 + 9sqrt(2))/(4*2 - 9)=(12+ 9sqrt(2))/(-1) = - 12 - 9sqrt(2)`

 

`(4 - 3sqrt(2))^2 = (4 - 3sqrt(2))*(4 - 3sqrt(2)) = 16 - 4*3sqrt(2) - 4*3sqrt(2) + (3sqrt(2))^2 = 16 - 24sqrt(2) + 18 = 34 - 24sqrt(2)`

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`sqrt(5b^2d) = bsqrt(5d)`

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oldnick | (Level 1) Valedictorian

Posted May 24, 2013 at 2:42 AM (Answer #2)

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`A) sqrt(18)/(sqrt(8)-3)=3sqrt(2)/(2sqrt(2)-3)=` `=3sqrt(2)/(2sqrt(2)-3) xx (2sqrt(2)+3)/(2sqrt(2)+3)` `=-(9sqrt(2)-12)`

`B)(4-3sqrt(2))^2=` `16-24sqrt(2)+18=2(17-12sqrt(2))`

`C) sqrt(5b^2d)=b sqrt(5d)`

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