Question

Efectuati :
a) ( 3/2√5+1/√20-5/√45 ) ori ( √5/3) la puterea -1
b) ( 5/√18+1/√2-√98 ) : ( -3/√2 ) la puterea -1
c) √3 ( 7/√3- 2:√75 -2/√27)

Answer 1

a) ( 3/2√5+1/√20-5/√45 ) × ( √5/3)⁻¹ =
= ( 3√5/10+√20/20-5√45/45 ) ×  3/√5 =
= ( 3√5/10+2√5/20-15√5/45 ) ×  3/√5 =
= ( 3√5/10+√5/10-√5/3 ) ×  3/√5 =
= ( 4√5/10 -√5/3 ) ×  3/√5 =
=12/10-1 =
=6/5-1
=1/5


b) ( 5/√18+1/√2-√98 ) : ( -3/√2 )⁻¹=
=( 15/√2+√2/2-7√2 ) : ( -√2/3 )=
=( 15√2/2+√2/2-7√2 ) : ( -√2/3 )=
=( 8√2-7√2 ) : ( -√2/3 )=
= √2 x ( -3/√2 )=
=-3

c) √3 ( 7/√3- 2/√75 -2/√27)  =
=√3 ( 7/√3- 2/5√3 -2/3√3)  =
= 7- 2/5-2/3  =
= (105-6-10)/15  =
=89/15