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What is the product of the radical expression (-5-√3) ^2 ?

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connorcolin3 | Valedictorian

Posted December 26, 2012 at 9:53 PM via web

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What is the product of the radical expression

(-5-√3) ^2 ?

Tagged with algebra trig, math

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jgeertz | College Teacher | (Level 1) Associate Educator

Posted December 27, 2012 at 12:39 AM (Answer #1)

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`(-5-sqrt3)^2`

Squaring an expression is the same as multiplying it 2 times.

`(-5-sqrt3) (-5-sqrt3)`

Now use the FOIL method.

`(-5*-5)(-5*-sqrt3)(-sqrt3*-5)(-sqrt3*-sqrt3)`

Simplify by multiplying and combining like terms.

`(25+10sqrt3+sqrt3^2)`

Raising a square root to the square power results in the expression inside the root.

`25+10sqrt3+3`

Add 3 to 25 to get 28.

`28+10sqrt3`

 `(-5-sqrt3)^2= 28+10sqrt3`

 

Sources:

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vaaruni | High School Teacher | Salutatorian

Posted December 31, 2012 at 7:05 AM (Answer #2)

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(-5-√3)2= {-(5+ √3)}2

            =(5+ √3) 2

            =(5)2+2*5*√3 +(√3)2 [Using formula (a+b)2=a2+2ab+b2]

            =  25 + 10√3 + 3

            =  28 + 10√3

   Hence,    (-5-√3)2  = 28 + 10√3  <--  Answer

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