[tex] \sqrt{(a- \sqrt{96}) ^{2} } + \sqrt{(b+ \sqrt{216}) ^{2} }+ \sqrt{(c- \sqrt{24}) ^{2} } \leq 0[/tex]
[tex]\sqrt{(a- \sqrt{96}) ^{2} }= (a- \sqrt{96}) ^{2* \frac{1}{2} } =a- \sqrt{96}[/tex]
[tex]\sqrt{(b+ \sqrt{216}) ^{2} }= (b+ \sqrt{216}) ^{2* \frac{1}{2} } =b+ \sqrt{216}[/tex]
[tex]\sqrt{(c- \sqrt{24}) ^{2} }= (c-\sqrt{24}) ^{2* \frac{1}{2} } =c- \sqrt{24}[/tex]
[tex](a- \sqrt{96}) + (b+ \sqrt{216}) + (c- \sqrt{24}) \leq 0[/tex]
[tex] \sqrt{96} = \sqrt{ 2^{5}*3 } = 2^{2} \sqrt{2*3} =4 \sqrt{6} [/tex]
[tex] \sqrt{216} = \sqrt{ 2^{3} * 3^{3} } =2*3* \sqrt{2*3} =6 \sqrt{6} [/tex]
[tex] \sqrt{24} = \sqrt{2 ^{3}*3 } =2 \sqrt{2*3} =2 \sqrt{6} [/tex]
[tex]a- 4\sqrt{6} + b+6 \sqrt{6} + c-2 \sqrt{6} \leq 0[/tex]
[tex]a+b+c- 6\sqrt{6} +6 \sqrt{6} \leq 0[/tex]
[tex]a+b+c \leq 0[/tex]
