1.
а) 3 √(1 ¹¹/₂₅) - 1 =3 √(³⁶/₂₅) - 1 = 3 * (⁶/₅) - 1 = 18 - 5 = 13/5 =2,6
5
б) √7,5 * √0,3 = √(7,5*0,3) =√2,25 =1,5
в) √250 = √(250/10) =√25 =5
√10
2.
а) 2√128 - √72 =2√(64*2) - √(36*2) =2*8√2 - 6√2 =16√2 -6√2=10√2
б) (3√2 + √50) √2 = 3√2 * √2 + √50 * √2 = 3*2 + √100 = 6+10 =16
в) (6-√3)²=6² -2*6*√3 +(√3)² =36-12√3 +3 =39-12√3
3.
а) 12√3 = √(12² * 3) =√(144*3) =√432
б) -8√5 = -√(8² * 5) = -√(64*5) = -√320
4.
√(а²-12а+36) = √(а-6)² = |a-6|
|5.9-6|= |-0.1|=0.1
5.
a) √10 - 5 = √5 * √2 - (√5)² = √5 (√2 - √5) = - √5 (√5 - √2) = - √5
√10 -2 √5 * √2- (√2)² √2 (√5 - √2) √2 (√5 - √2) √2
б) 25-b = 5² - (√b)² = (5 - √b)(5 + √b) = 5 - √b
√b +5 √b + 5 5 + √b
6.
4 + 4 = 4(3 - √15) +4 (3+√15) =
3+√15 3-√15 (3+√15)(3-√15)
=12 -4√15 +12 +4√15 = 24 = 24 = -4
3² - (√15)² 9-15 -6