Mapel : matematika Bab : bentuk pangkat dan bentuk akar

Mapel : matematika Bab : bentuk pangkat dan bentuk akar

Matematika :

Tentukan hasil operasi berikut.

$a.) : 12 sqrt{27} - 2 sqrt{48} + sqrt{75} \ = 12 sqrt{9 times 3} - 2sqrt{16 times 3} + sqrt{25 times 3} \ = 12 times 3 sqrt{3} -2 times 4 sqrt{3} + 5 sqrt{3} \ = 36 sqrt{3} - 8 sqrt{3} + 5 sqrt{3} \ = (36 - 8 + 5) sqrt{3} \ = 33 sqrt{3} \ \ b.) : (3 sqrt{5} - sqrt{50} ) times sqrt{160} \ = (3 sqrt{5} - sqrt{25 times 2} ) times sqrt{16 times 10} \ = (3 sqrt{5} - 5 sqrt{2} ) times 4 sqrt{10} \ = 12 sqrt{50} - 20 sqrt{20} \ = 12 sqrt{25 times 2} - 20 sqrt{4 times 5} \ = 12 times 5 sqrt{2} - 20 times 2 sqrt{5} \ = 60 sqrt{2} - 40 sqrt{5} \ \ c.) frac{ sqrt{63} }{ sqrt{28} } times ( sqrt{7} + sqrt{112} ) \ = frac{ sqrt{9 times 7} }{ sqrt{4 times 7} } times ( sqrt{7} + sqrt{16 times 7} ) \ = frac{ 3sqrt{7} }{2 sqrt{7} } times ( sqrt{7} + 4 sqrt{7}) \ = frac{ 3sqrt{7} }{2 sqrt{7} } times 5 sqrt{7} \ = frac{15 sqrt{7} }{2 sqrt{7} } \ = frac{15}{2} sqrt{7}$

A) 12√27 – 2√48 + √75
= 12×3√3 – 2×4√3 + 5√3
= (36+5-8)√3
= 33√3

b) (3√5 – √50) x √160
= ( 3√5 – 5√2) x 4√10
= 12√50 – 20√20
= 12×5√2 – 20×2√5
= 60√2 – 40√5
= 20(3√2 – 2√5)

c) √63/√28 x ( √7 + √112)
= √(9×7)/√(4×7) x ( √7 + 4√7)
= 3√7/2√7 x 5√7
= (15√7)/2