a) 3√18 - √32 + 4√2 + √162 = 9√2 - 4√2 + 4√2 + 9√2 = (9-4+4+9)√2 = 18√2
b) 2√48 - 4√27 +√75 +√12 = 8√3 - 12√3 + 5√3 + 2√3 = (8-12+5+2)√3 = 3√3
c) √80 + √20 - √5 + 5√45 = 4√5 + 2√5 - √5 + 15√5 =(4+2-1+15)√5 = 20√5
d) 3√2 (√50 - 2√18 + √98) = 3√2 ( 5√2 - 6√2 + 7√2) = 3√2. 6√2 = 36
e) √27 -3√48+ 2√108 -√(2-√3)² = 3√3 - 12√3 + 12√3 - 2 + √3 = (3-12+12+1)√3 -2 =4√3 -2
f) (3-√2)(3+√2) = 9-2 =7
g) (√20 -3√10 +√5)√5 +15√2 = (2√5 - 3√10 + √5)√5 + 15√2 = (3√5 - 3√10)√5 + 15√2 = 15 - 3√50 +15√2 = 15 - 15√2 + 15√2 = 15
h) 5√18 - √50 + √8 + √(1/2) = 15√2 - 5√2 + 2√2 + 1/√2 = (15-5+2)√2 + √2/2 = 2√2 +√2/2 = (4√2 + √2)/2 = 5√2/2