∵ (√(11)+5√12)(√(11)-5√(12))
∴ (11 - 5√(132) + 5√(132) - 25√(144)).......(FOIL)
∴ (11 - (25)(12)).......(combine like terms)
∴ (11 - 300).......(expand)
∴ -289 <------------------(ANSWER)
-289
it's a difference in squares
((1)√11+5√12)((1)√11-5√12) = (1)(11)-(25)(12)
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∵ (√(11)+5√12)(√(11)-5√(12))
∴ (11 - 5√(132) + 5√(132) - 25√(144)).......(FOIL)
∴ (11 - (25)(12)).......(combine like terms)
∴ (11 - 300).......(expand)
∴ -289 <------------------(ANSWER)
-289
it's a difference in squares
((1)√11+5√12)((1)√11-5√12) = (1)(11)-(25)(12)