Réponse :
Explications étape par étape
Bonjour,
Simplifier les nombres suivants :
A = [(2 x 10^(-5))^3 x 2,5]/(5 x 20^(-4))^2
A = (2^3 x 2,5 / 5^2) x 10^(-5x3) / (2 x 10)^(-4x2)
A = 2^3 x 5^2 x 5 / 2 x 10^(-15) / (2^(-8) x 10^(-8))
A = 2^(3-1+8) x 5^(2+1) x 10^(-15+8)
A = 2^10 x 5^3 x 10^(-7)
A = 2^10 x 5^3 x (2 x 5)^(-7)
A = 2^(10-7) x 5^(3-7)
A = 2^3 x 5^(-4)
B = (1/16)^(-3) x 12^(-4) x (0,09 x 10^9)^2
B = 16^3 x (3 x 4)^(-4) x (9/100 x 10^9)^2
B = (4 x 4)^3 x 3^(-4) x 4^(-4) x 9^2 x 10^(9x2) x 10^(-2x2)
B = 4^(2x3-4) x 3^(-4) x 3^(2x2) x 10^(18-4)
B = 4^(6-4) x 3^(-4+4) x 10^14
B = 4^2 x 3^0 x 10^14
B = 4^2 x 10^14
B = 2^(2x2) x (2 x 5)^14
B = 2^(4+14) x 5^14
B = 2^18 x 5^14
2) en comparant leur carré déterminer si les nombres réels donnés sont égaux :
5V2 et 2V5
(5V2)^2 = 5^2 x (V2)^2 = 25 x 2 = 50
(2V5)^2 = 2^2 x (V5)^2 = 4 x 5 = 20
[tex]5\sqrt{2} \ne 2\sqrt{5}[/tex]
1/V3 et V3/3
(1/V3)^2 = 1^2/(V3)^2 = 1/3
(V3/3)^2 = (V3)^2/3^2 = 3/9 = 1/3
1/V3 = V3/3
V(3 + 2V2) et 1 + V2
(V(3 + 2V2)^2 = 3 + 2V2
(1 + 2V2)^2 = 1^2 + 2 x 1 x 2V2 x (2V2)^2 = 1 + 4V2 + 6 = 7 + 4V2
[tex]\sqrt{3 + 2\sqrt{2}} \ne 1 + \sqrt{2}[/tex]
Simplifier les écritures :
A = (V(3V3))^4
A = (3V3)^2
A = 3^2 x (V3)^2
A = 9 x 3
A = 27
B = (V(2/V7))^4
B = (2/V7)^2
B = 2^2/(V7)^2
B = 4/7
C = 5/V5 x (2/V5)^3
C = 5 x 2^3 x 1/(V5)^(1+3)
C = 5 x 8 x 1/(V5)^4
C = 8 x 5 x 1/5^2
C = (8 x 5)/(5 x 5)
C = 8/5
D = V(4/25) + V(36/25)
D = V(2^2/5^2) + V(6^2/5^2)
D = 2/5 + 6/5
D = (2 + 6)/5
D = 8/5
E = V(1/100) + V(49/25)
E = 1/V(10^2) + V(7^2/5^2)
E = 1/10 + 7/5
E = 1/10 + (7 x 2)/(5 x 2)
E = 1/10 + 14/10
E = (1 + 14)/10
E = 15/10
E = (3 x 5)/(2 x 5)
E = 3/2
F = V((9/8)/2) + V(1/(1/81))
F = V(9/8 x 1/2) + V(1 x 81)
F = V(3^2 x 2^4) + V(9^2)
F = 3 x 2^2 + 9
F = 3 x 4 + 9
F = 12 + 9
F = 21
