Exercice 1 :
√50 + 2√32 - 4√72
= √25*√2 + 2*√16*√2 - 4*√36√2
= 5√2 + 2*4*√2 - 4*6*√2
= 5√2 + 8√2 - 24√2
= -11√2
2√75 - 3√48 + 2√243
= 2*√25*√3 - 3*√16*3 + 2*√81*√3
= 2*5*√3 - 3*4*√3 + 2*9*√3
= 10√3 - 12√3 + 18√3
= 16√3
Exercice 2 :
A= √48 + √20
= √16*√3 + √4*√5
= 4√3 + 2√5
B = √108 - √45
= √36*√3 - √9*√5
= 6√3 - 3√5
Exercice 3 :
(√5-√3)² = (√5)² - 2*√5*√3 + (√3)² = 5 - 2√15 + 3 = 8 - 2√15
(2√3 - √2)(2√3 + √2) = (2√3)² - (√2)² = 12 - 2 = 10
1/√7 = (1*√7) / (√7*√7) = √7 / 7
√2 / (√5 - √3) = √2*(√5+√3) / (√5-√3)(√5+√3) = √10+√6 ) / (√5)²-(√3) = √10+√6 ) / 2
