Question

Calculati:
a) 2√3/3-5/√3
b)(2√6)–¹+2/√3
c)(4√5/5-3/2√5):(-√20/3)
d)1/3√2+5√2/√6

Answer 1

a) 2√3/3-5/√3=
2√3/3-5√3/(√3·√3)=
2√3/3-5√3/3=-3√3/3=-√3

b)(2√6)–¹+2/√3=
1/2√6+2/√3=
√6/(2·√6·√6)+2√3/(√3·√3)=
√6/12+2√3/3=
√6/12+(4·2√3)/3=
(√6+8√3)/12=√3(√2+8)/12

c)(4√5/5-3/2√5):(-√20/3)=
(4√5/5-3√5/10):(-2√5)/3)=
[2·4√5-3√5)/10]·(-3/2√5)=
[(8√5-3√5)/10]·(-3/2√5)=
5√5/10·(-3/2√5)=
√5/2·(-3/2√5)=-3/4

d)1/3√2+5√2/√6=
√2/(3·√2·√2)+(5·√2·√6)/(√6·√6)=
√2/6+5√12/6=
√2/6+5·2√3/6=
√2/6+10√3/6=
√2/6+5√3/3