Question

a) √5*{5/3√5+√0,(5)+√20}--√6*{√0,(6)+2√2/√3}
b) (14/3√7-15/2√175)+(3√28/4-2/√63)+(√7/2-14/√28)
c) 6√20/7√5 *{3/2√54+√0,1(6)-5/√6}

Answer 1

a) √5*{5/3√5+√0,(5)+√20}-√6*{√0,(6)+2√2/√3} =
0,(6)=6/9=2/3
0,(5)=5/9
=√5*{5/3√5+√(5/9)+2√5}-√6*{√(2/3)+2√2/√3} =
=√5*{5/3√5+√5/3)+2√5}-√6*{√2/√3)+2√2/√3} =
=5/3+5/3+10-√6*3√2*√3/3 =
=10/3+4 =22/4=7(3)


b) (14/3√7-15/2√175)+(3√28/4-2/√63)+(√7/2-14/√28)=
=(14/3√7-15/10√7)+(12√7/4-2/3√7)+(√7/2-14/2√7)=
=(14√7/21-15√7/70)+(12√7/4-2√7/21)+(√7/2-14√7/14)=
=(2√7/3-3√7/14)+(3√7-2√7/21)+(√7/2-√7)=
=2√7/3-3√7/14+2√7-2√7/21+√7/2=
=√7(2/3-3/14+2-2/21+1/2)=
=√7(28-9+84-4+21)/42=
=120√7/42=
=20√7/7

=c) 6√20/7√5 *{3/2√54+√0,1(6)-5/√6}=
=12√5/7√5 *{3/6√6+√0,1(6)-5/√6}=
0,1(6)=(16-1)/90=15/90=1/6
=12/7 *{3√6/36+1/√6-5/√6}=
=12/7 *{√6/12+√6/6-5√6/6}=
=12/7 *{√6/12-4√6/6}=
=12/7 *{√6/12-8√6/12}=
=12/7 *{-7√6/12}=
=-√6