Question

Rationalizati numitorii fractiilor:
a)1/3+√2
b)2/3+2√2
c)3/2√3-1
d)4/√5+√2
e)5/√2+√3
f)1/2√3+3√2

Answer 1

a)1/(3+√2)=(3-√2)/(3+√2)(3-√2)=(3-√2)/(9-2)=(3-√2)/7
b)2/(3+2√2)=2(3-2√2)/(3+2√2)(3-2√2)=2(3-2√2)/(9-2·2·2)=2(3-2√2)
c)3/(2√3-1)=3(2√3+1)/(2√3-1)(2√3+1)=3(2√3+1)/(4·3-1)=3(2√3+1)/11
d)4/(√5+√2)=4(√5-√2)/(√5+√2)(√5-√2)=4(√5-√2)/(5-2)=4(√5+√2)/3
e)5/√2+√3)=5(√2-√3)/(√2+√3)(√2-√3)=5(√2-√3)(2-3)=-5(√2-√3)=5(√3-√2)
f)1/(2√3+3√2)=(2√3-3√2)/(2√3+3√2)(2√3-3√2)=(2√3-3√2)/(12-18)=-(2√3-3√2)/6=
(3√2-2√3)/6=√2/2-√3/3