РОЗДІЛ 3. Квадратні корені. Дійсні числа » 569

569. Спростіть вираз: 1) (√45- √4,5)/(√10-1) = (√(4,5•10)- √4,5)/(√10-1) = (√4,5(√10-1))/(√10-1) = √4,5; 2) (√48+ 2√2)/(√6+1) = (√(8•6)+ √8)/(√6+1) = (√8(√6+1))/(√6+1) = √8; 3) (√3- √27)/(√0,12+ √3) = (√3- √(9•3))/(√(0,04•3)+√3) = (√3- 3√3)/(0,2√3+√3) = (√3(1-3))/(√3(0,2+1)) = (-2)/1,2 = –20/12 = –5/3 = –12/3; 4) (√225+ 2√625)/√169 = (15+2 •25)/13 = 65/13 = 5; 5) (√0,3-√0,6)/(1- √2) = (√0,3-√(0,3•2))/(1- √2) = √(0,3(1- √2))/(1- √2) = √0,3; 6) (√4,41- 2√2,1+ 1)/( 1- √2,1) = (〖(√(2,1))〗^2- 2√2,1 •1+ 1^2)/(1- √2,1) = 〖(√2,1-1)〗^2/(1- √2,1) = 〖(1- √(2,1))〗^2/(1- √2,1) = 1 – √2,1. 7) (√1,44+ 2√3,6+ 3)/(√3+ 2√0,3) – 0,4√7,5 = (〖(√1,2)〗^2+ 2• √3 • √1,2+ (√3 )^2)/(√3+ √1,2) – √(0,16•7,5) = ((√1,2+ √3 )^2)/(√3+ √1,2) – √1,2 = √1,2 + √3 – √1,2 = √3; 8) 2^(\5-2√6)/(5+2√6) + 2^(\5+2√6)/(5-2√6) = (10-4√6+ 10+4√6)/((5+2√6)(5-2√6)) = 20/(25-(2√6 )^2 ) = 20/(25-24) = 20/1 = 20; 9) (√5+ 1)/√15 – 1^(\√5)/√3 = (√5+ 1- √5)/√15 = 1/√15; 10) 1^(\8-2√7)/(8+2√7) + 1^(\8+2√7)/(8-2√7) = (8-2√7+ 8+2√7)/((8+2√7)(8-2√7)) = 16/〖64-(2√7)〗^2 = 16/(64-28) = 16/34 = 4/9.