Question

Raționalizați numitorii:
a) $\frac{ \sqrt{2} }{2+ \sqrt{2} }$
b) $\frac{ -\sqrt{2} }{3-2 \sqrt{2} }$
c) $\frac{ \sqrt{15} }{ \sqrt{3}- \sqrt{5} }$
d) $\frac{12}{ \sqrt{7}+ \sqrt{3} }$
e) $\frac{3 \sqrt{7}-3 \sqrt{5} }{2 \sqrt{7}-2 \sqrt{5} }$
f) $\sqrt{ \frac{3- \sqrt{15} }{3+ \sqrt{5} } }$

Answer 1

a) rationalizam cu 2-√2 
√2(2-√2)/(2+√2)(2-√2)
2√2-√4/2²-(√2)²
2√2-2/4-2
2(√2-1)/2= √2-1
b)rationalizam cu 3+2√2
-√2(3+2√2)/(3+2√2)(3-2√2)
-2√3-2√4/3²-(-2√2)²
-2√3-4/9+8
-2(√3+2)/17
c) rationalizam cu √3+√5
√15(√3+√5)/(√3+√5)(√3-√5)
√45+√75/√3²-√5²
3√5+5√3/3-5
3√5-5√3/-2
d) rationalizam cu √7-√3
12(√7-√3)/ (√7-√3)(√7+√3)
12√7-12√3/√7²-√3²
12(√7-√3)/4=3(√7-√3)
e) rationalizam cu  2√7+2√5
(3√7-3√5)(2√7+2√5)/(2√7+2√5)(2√7-2√5)
6√14-6√25/(2√7)²-(2√5)²
6√14-30/28-20
6√14-30/8=2(3√14-15)/8=3√14-15/4 
f) rationalizam cu  √3-√5
(3-√15)(√3-√5)/(√3-√5)(√3+√5)
3√3-3√5-√45+√75/(√3)²-(√5)²
3√3-3√5-3√5+5√3/9-5
8√3-6√5/ 4=2(4√3-3√5)/4=4√3-3√5/2
 Succes!! Sper ca ti-am fost de ajutor !