№ 4.105
а) √2/2 = (√2*√2)/(2*√2) = 2/(2√2) = 1/√2
б) √6/3 = (√6*√6)/(3*√6) = 6/(3√6) = 2/√6
в) √5/5 = (√5*√5)/(5√5) = 5/(5√5) = 1/√5
г) √10/5 = (√10√10)/5√10 = 10/(5√10) = 2/√10
№ 4.106
а) (√6 - 2)/2 = [(√6 - 2)(√6 + 2)]/[2(√6 + 2)] = (6 - 4)/[2(√6 + 2) = 1 / (√6 + 2)
б) (√3 - 1)/2 = [(√3 - 1)(√3 + 1)]/[2(√3 + 1)] = (3 - 1)/[2(√3 + 1)] = 1/(√3 + 1)
в) (3 + √2)/2 = [(3 + √2)(3 - √2)]/[2(3 - √2)] = (9 - 2)/[(2(3 - √2)] = 7/[2(3 - √2)]
г) (√7 + √2)/5 = [(√7 + √2)(√7 - √2)]/[5(√7 - √2)] = (7 - 2)/[5(√7 - √2)] =
= 1 / (√7 - ³2)