'difference of squares' jumps to mind
(7-5)=(sqrt7+sqrt5)*(sqrt7-sqrt5)
lets see what happens when we multiply by(sqrt7+sqrt5) /(sqrt7+sqrt5)
(sqrt7+sqrt5)(sqrt7+sqrt5) / (7-5)
(7+2(sqrt7*sqrt5)+5)/2
(12+2sqrt35)/2
6+sqrt35
multiply top and bottom by â7 + â5 to get 6 + â35
â(7)+â(5) / â(7)-â(5) times â(7)+â(5)/â(7)+â(5)
{â(7)+â(5)* â(7)+â(5)} over {â(7)-â(5) * â(7)+â(5)}
{(â7)^2 + 2*â7*â5+ (â5)^2} over (â7)^2 - (â5)^2
7+2â35+5 over 7-5
12+ 2â35 over 2
6+â35
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Verified answer
'difference of squares' jumps to mind
(7-5)=(sqrt7+sqrt5)*(sqrt7-sqrt5)
lets see what happens when we multiply by(sqrt7+sqrt5) /(sqrt7+sqrt5)
(sqrt7+sqrt5)(sqrt7+sqrt5) / (7-5)
(7+2(sqrt7*sqrt5)+5)/2
(12+2sqrt35)/2
6+sqrt35
multiply top and bottom by â7 + â5 to get 6 + â35
â(7)+â(5) / â(7)-â(5) times â(7)+â(5)/â(7)+â(5)
{â(7)+â(5)* â(7)+â(5)} over {â(7)-â(5) * â(7)+â(5)}
{(â7)^2 + 2*â7*â5+ (â5)^2} over (â7)^2 - (â5)^2
7+2â35+5 over 7-5
12+ 2â35 over 2
6+â35