Răspuns:
a) 2√3+3√5
b) 0
Explicație pas cu pas:
Se scrie exericitiul si se ridica radicalurile de la numitor la numarator, se aduce la acelasi numitor in paranteze, se inmulteste cu ce este in afara parantezei si apoi se fac restul calculelor, astfel:
a) (1/√3+1/√2)*√6+(1/√5+1/√3)*√15+(1/√2-1/√5)*√10=(√3/3+√2/2)*√6+(√5/5+√3/3)*√15+(√2/2-√5/5)*√10= (se aduce la acelasi numitor)
=(2√3/6+3√2/6)*√6+(3√5/15+5√3/15)*√15+(5√2/10-2√5/10)*√10=2√18/6+3√12/6+3√75/15+5√3/15
5√20/10-2√50/10=(6√2+6√3)/6+(15√3+15√5)/15+(20√5-10√2)/10=√2+√3+√3+√5+2√5-√2=2√3+3√5
b) (2/3√6-1/2√6)*√6+(√24-5/2√6)*√6-29/3=(2√6/3√6-√6/2√6)+(√144-5√6/2√6)-29/3=(2/3-1/2)+(12-5/2)-29/3=(4-3)/6+(24-5)/2-29/3=1/6+19/2-29/3=1/6+57/6-58/6=0
