[tex]x= \sqrt{8+2 \sqrt{7} } [/tex]
[tex]x= \sqrt{8+ \sqrt{28} } [/tex]
Avem formula:
[tex]x= \sqrt{a+ \sqrt{b} }= \sqrt{ \frac{a+c}{2} } + \sqrt{ \frac{a-c}{2} } [/tex]
[tex]c= \sqrt{ a^{2}-b } [/tex]
[tex]c= \sqrt{8^{2}-28 }= \sqrt{64-28}= \sqrt{36}=6[/tex]
[tex]x= \sqrt{ \frac{8+6}{2} }+ \sqrt{ \frac{8-6}{2} }= \sqrt{ \frac{14}{2} }+ \sqrt{ \frac{2}{2} }= \sqrt{7}+ \sqrt{1}= \sqrt{7}+1[/tex]
[tex] x= \left[\begin{array}{ccc} \sqrt{7}+1 \end{array}\right] [/tex]
