سلسلة تمارين رقم 3

A = √18

B = √50 + 2√8

C = √27 - √12

D = √(3² + 4²)

الحل:

A = √(9×2) = 3√2

B = √(25×2) + 2√(4×2) = 5√2 + 2(2√2) = 5√2 + 4√2 = 9√2

C = √(9×3) - √(4×3) = 3√3 - 2√3 = √3

D = √(9 + 16) = √25 = 5

E = 1 / √2

F = 3 / (√5 - 1)

G = (√3 + 1) / (√3 - 1)

الحل:

E = (1 × √2) / (√2 × √2) = √2 / 2

F = 3(√5 + 1) / [(√5 - 1)(√5 + 1)] = 3(√5 + 1) / (5 - 1) = 3(√5 + 1) / 4

G = (√3 + 1)² / [(√3 - 1)(√3 + 1)] = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3) / 2 = 2 + √3