Задача 45142 ...

vk396216921

2020-03-19 21:50:42

Упростите выражение :
1)√1200-20√2,43+4,5√0,48
2)√20/81-2/9√45/49-11/20√80/121

sova

2020-03-19 22:05:27

★

1)
1200=400*3
sqrt(1200)=sqrt(400*3)=sqrt(400)*sqrt(3)=20sqrt(3)

sqrt(2,43)=[m]\sqrt{\frac{243}{100}}=\sqrt{\frac{81\cdot 3}{100}}[/m]=[m]\frac{9}{10}[/m]sqrt(3)

sqrt(0,48)=[m]\sqrt{\frac{48}{100}}=\sqrt{\frac{16\cdot 3}{100}}[/m]=[m]\frac{4}{10}[/m]sqrt(3)

√1200–20√2,43+4,5√0,48=20sqrt(3)-18sqrt(3)+1,8sqrt(3)=3,8sqrt(3)

2)
[m]\sqrt{\frac{20}{81}}-\frac{2}{9}\sqrt{\frac{45}{49}}-\frac{11}{20}\sqrt{\frac{80}{121}}=\sqrt{\frac{4\cdot 5}{81}}-\frac{2}{9}\sqrt{\frac{5\cdot 9}{49}}-\frac{11}{20}\sqrt{\frac{16\cdot 5}{121}}=[/m]

[m]=\frac{2}{9}\sqrt{5}-\frac{2}{9}\cdot \frac{3}{7}\sqrt{5}-\frac{11}{20}\cdot \frac{4}{11}\sqrt{5}=\frac{2}{9}\cdot \frac{4}{7}\sqrt{5}-\frac{1}{5}\sqrt{5}=-\frac{23}{315}\sqrt{5}[/m]