+0  
 
0
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3
avatar+546 

(6-sqrt12)(6+sqrt12)

and...

 

(3+sqrt8)(3-sqrt8)

 Jul 28, 2014

Best Answer 

 #1
avatar+4473 
+10

(6-sqrt12)(6+sqrt12)

FOIL: 36 + 6sqrt(12) - 6sqrt(12) - 12 = 36 - 12 = 24.

 

(3+sqrt8)(3-sqrt8)

FOIL: 9 + 3sqrt(8) - 3sqrt(8) - 8 = 9 - 8 = 1.

 

Note: It may be easier to notice that both of these are a "difference of squares:"

(6-sqrt12)(6+sqrt12) is in the format (a - b)(a + b) = (a^2 - b^2) since the two middle terms [ab & -ab] cancel out.

(a^2 - b^2) --> (6^2 - (sqrt(12)^2)) --> (36 - 12) = 24.

Same for the second one --> (3^2 - (sqrt(8))^2) = (9 - 8) = 1.

 Jul 28, 2014
 #1
avatar+4473 
+10
Best Answer

(6-sqrt12)(6+sqrt12)

FOIL: 36 + 6sqrt(12) - 6sqrt(12) - 12 = 36 - 12 = 24.

 

(3+sqrt8)(3-sqrt8)

FOIL: 9 + 3sqrt(8) - 3sqrt(8) - 8 = 9 - 8 = 1.

 

Note: It may be easier to notice that both of these are a "difference of squares:"

(6-sqrt12)(6+sqrt12) is in the format (a - b)(a + b) = (a^2 - b^2) since the two middle terms [ab & -ab] cancel out.

(a^2 - b^2) --> (6^2 - (sqrt(12)^2)) --> (36 - 12) = 24.

Same for the second one --> (3^2 - (sqrt(8))^2) = (9 - 8) = 1.

AzizHusain Jul 28, 2014
 #2
avatar+546 
0

thanks a  million Aziz!!!!

 Jul 28, 2014
 #3
avatar+546 
0

BTW your answers are CORRECT for these 2!!!!!!!! 

 Jul 28, 2014

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