(√5 - √15)^2 = (√5 - √15)(√5 - √15)Expanding using the FOIL method:= (√5)(√5) - (√5)(√15) - (√15)(√5) + (√15)(√15)= 5 - √75 - √75 + 15= 20 - 2√75= 20 - 2√(253)= 20 - 2√25√3= 20 - 25√3= 20 - 10√3
Therefore, (√5 - √15)^2 = 20 - 10√3.
(√5 - √15)^2 = (√5 - √15)(√5 - √15)
Expanding using the FOIL method:
= (√5)(√5) - (√5)(√15) - (√15)(√5) + (√15)(√15)
= 5 - √75 - √75 + 15
= 20 - 2√75
= 20 - 2√(253)
= 20 - 2√25√3
= 20 - 25√3
= 20 - 10√3
Therefore, (√5 - √15)^2 = 20 - 10√3.