Question

Calculati:
a)[tex]( \frac{3}{2 \sqrt{3} } + \sqrt{ \frac{0,2(6)}{1,8} }) * \frac{1}{4,(3) };
[/tex]
b)[tex]( \sqrt{ \frac{0,8}{0,2(7)} }- \frac{3}{2 \sqrt{2} }): \frac{1}{3,(3)};
[/tex]
c)($(\sqrt{ \frac{0,8(3)}{2,(6)}:0,3 }+ \frac{1}{ 6\sqrt{6} }) : \frac{1}{1,5};$
d)([tex](\frac{4}{ \sqrt{5} }- \sqrt{0,75: \frac{3,0(5)}{1,8(3)} })* \frac{1}{3,5} .
[/tex]
Multumesc mult!!

Answer 1

a)
0,2(6)=(26-2)/90=24/90=4/15
1,8=18/10 =9/5
4/15 : 9/5=4/15 ×5/9=4/27
4,(3)=(43-4)/9=39/9=13/3    
[3/2√3+√0,2(6)/1,8] × 1/4,(3)=(3/2√3+√4/27) × 1/(13/3)=
=(3/2√3+2/3√3) × 3/13=(9+4)/6√3 × 3/13=13/6√3 × 3/13=1/2√3=√3/6

b)0,8=8/10=4/5
0,2(7)=(27-2)/90=25/90=5/18
4/5 :5/18=4/5 ×18/5=72/25
3,(3)=(33-3)/9=30/9=10/3
{√[0,8/0,2(7)] - 3/2√2} : 1/3,(3)=
={√72/25 - 3√2/4} : 1/(10/3)=
={6√2/5 - 3√2/4} ×3/10=
=(24√2- 15√2)/20 ×3/10=
=9√2/20 ×3/10=27√2/200


c)0,8(3)=(83-8)/90=75/90=5/6
2,(6)=(26-2)/9=24/9=8/3
0,3=3/10
5/6:8/3:3/10=5/6×3/8:3/10=5/16 ×10/3=50/48
1,5=15/10=3/2
{√[0,8(3)/2,(6) :0,3]+1/6√6}:1/1,5=
={√50/48+√6/36}:1/(3/2)=
={5√2/4√3+√6/36}: 2/3=
={5√6/12+√6/36} × 3/2=
=(15√6+√6)/36} × 3/2=
=4√6/9 × 3/2=
=2√6/3

d)
0,75=3/4
3,0(5)=(305-30)/90=275/90=55/18
1,8(3)=(183-18)/90=165/90=33/18
3,0(5)/1,8(3)=55/18 : 33/18=55/18×18/33=5/3
1/3,5=10/35=2/7
{4/√5 -√[(0,75:3,0(5)/1,8(3)] } *1/3,5=
=[4√5/5 -√(3/4: 5/3)] *2/7=
=[4√5/5 -√(3/4 ×3/5)] *2/7=
=[4√5/5 -3/2√5)] *2/7=
=[4√5/5 -3√5/10)] *2/7=
=(8√5 -3√5)/10 *2/7=
=5√5 /10 *2/7=
=√5/2 *2/7=√5/7