Explications étape par étape :
Bonjour
EX4/ 1.
√25 = 5
√100 = √10² = 10
√0 = 0
√81 =√9² = 9
√1 = 1
2.a √27 = [tex]\sqrt{3^{2} * 3}[/tex] = 3√3
√200 = [tex]\sqrt{2^{2}*2*5^{2} }[/tex] = 2 * 5 √2 = 10√2
√252 = [tex]\sqrt{2^{2} *3^{2} *7}[/tex] = 2 * 3 √7 = 6√7
b. √98 = [tex]\sqrt{2*7^{2} }[/tex] = 7√2
√150 = [tex]\sqrt{2*3*5^{2} }[/tex] = 5√6
√845 = [tex]\sqrt{5 * 13^{2} }[/tex] = 13√5
EX5
a. 2√3 * 6√3 = 12 * √9 = 12 * 3 = 36
2√5 * 4√15 = 8√75 = 8[tex]\sqrt{3*5^{2} }[/tex] = 8*5√3 = 40√3
b. √5 * 2√45 = √5 * 2[tex]\sqrt{3^{2}*5 }[/tex] = √5 * 6√5 = 6√25 = 6 * 5 = 30
3√6 * √42 = 3√252 = 3 * 6√7 = 18√7
EX6
a = 2√3 - 5√3 +√3
⇔ a = -2√3
b = √45 + 2√5 - 3√20
⇔ b = 3√5 + 2√5 - 6√5
⇔ b = -√5
c = 2√7 - 9√7 + 4√7
⇔ c = -3√7
d = 3√5 - 5√45 + 4√20 - 13√125
⇔ d = 3√5 - 5 * 3√5 + 4 * 2√5 - 13 * 5√5
⇔ d = 3√5 - 15√5 + 8√5 - 65√5
⇔ d = -69√5
