Question

a)√2·(4 supra √18 +√0,(2))+√3·(√0,(3)+2 supra √3)=
b)√5·(5 supra 3√5+√0,(5)+√20 supra 6)-√6·(√0,(6)+2√2 supra √3)=
c)(14 supra 3√7-15 supra 2√175)+(3√28 supra 4-2 supra √63)+(√7 supra 2-14 supra √28)=
d)6√20 supra 7√5·(3 supra 2√54+√0,1(6) -5 supra √6)=
e)√2·(4 supra √18+√0,(2))+√3·(√0,(3)+2 supra √3)=
f)√3·(1 supra √3+5√3 supra 6)-1 supra √3·(12 supra 2√3+4√3 supra 5)-(24 supra 10√3-√12 supra 4):1 supra √27

Answer 1

a)√2·(4/√18 +√0,(2))+√3·(√0,(3)+2/√3)=
0,(2)=2/9
0,(3)=3/9=1/3
=√2·[(4/3√2 +√(2/9)]+√3·(√1/3+2/√3)=
=√2·(2√2/3 +√2/3)+√3·[√(1/3)+2/√3]=
=√2·√2+√3·[1/√3+2/√3]=
=2 +1+2=
=4


b)√5·(5/3√5+√0,(5)+√20/6)-√6·(√0,(6)+2√2/√3)=
0,(5)=5/9
0,(6)=6/9=2/3
=√5·[5/3√5+√(5/9)+2√5/6]-√6·[√(2/3)+2√2/√3)=
=5/3+5/3+5/3-√6·(√2/√3+2√6/3)=
=5-√6·(√6/3+2√6/3)=
=5-√6·3√6/3=
=5-6=-1

c)(14/3√7-15/2√175)+(3√28/4-2/√63)+(√7/2-14/√28)=
=(14/3√7-15/10√7)+(6√7/4-2/3√7)+(√7/2-14/2√7)=
=(14√7/21-15√7/70)+(3√7/2-2√7/21)+(√7/2-14√7/14)=
=2√7/3-3√7/14+3√7/2-2√7/21+√7/2-√7=
=2√7/3-3√7/14+4√7/2-2√7/21-√7=
=(28√7-9√7+84√7-4√7-42√7)/42=
=57√7/42=19√7/14


d)6√20/7√5·(3/2√54+√0,1(6) -5/√6)=
0,1(6)=(16-1)/90=15/90=1/6
=12√5/7√5·[3/6√6+√(1/6) -5/√6]=
=12/7·[3√6/36+√6/6 -5√6/6]=
=12/7·[3√6/36 -4√6/6]=
=12/7·[3√6/36 -24√6/36]=
=12/7·(-21√6/36)=
=12/7·(-7√6/12)=
=12/7·(-7√6/12)=
=-√6

e)√2·(4/√18+√0,(2))+√3·(√0,(3)+2/√3)=
=√2·[4/3√2+√(2/9)+√3·(√(1/3)+2/√3)=
=√2·[4/3√2+√2/3+√3·(1/√3)+2√3/3)=
=4/3+2/3+1+2=
=6/3+3=
=5

f)√3·(1/√3+5√3/6)-1/√3·(12/2√3+4√3/5)-(24/10√3-√12/4):1/√27=
=1+5/2-2-4/5-(12/5√3-√3/2):1/3√3=
=1+2,5-0,8-(12√3/5*3-√3/2):√3/9=
=2,7-(4√3/5-√3/2):√3/9=
=2,7-7,2+4,5=
=0