[tex] \sqrt{19- 6\sqrt{2}} =[/tex]
aplicam formula radicalilor compusi
[tex]\sqrt{a-\sqrt{b}}= \sqrt{ \frac{a+ \sqrt{a^{2}-b}}{2}}- \sqrt{ \frac{a- \sqrt{a^{2}-b}}{2}}[/tex]
[tex]a=19, b=6 \sqrt{2} = \sqrt{72} \\ \\ = \sqrt{ \frac{19+ \sqrt{361-72}}{2}}- \sqrt{ \frac{19- \sqrt{361-72}}{2}} \\ \\ =\sqrt{ \frac{19+ \sqrt{289}}{2}}- \sqrt{ \frac{19- \sqrt{289}}{2}} \\ \\ \sqrt{289}=17 \\ \\ \sqrt \frac{36}{2}-1= \sqrt{18} -1=3 \sqrt{2}-1 [/tex]
