[tex]\sqrt{24 } - ( \sqrt{6} + (8 \sqrt{6} + \sqrt{384))} [/tex]
[tex] = 2 \sqrt{6} - ( \sqrt{6} + (8 \sqrt{6} + 8 \sqrt{6} ))[/tex]
[tex]= 2 \sqrt{6} - ( \sqrt{6} + 16 \sqrt{6}) [/tex]
[tex] = 2 \sqrt{6} - 17 \sqrt{6} [/tex]
[tex] = - 15 \sqrt{6} [/tex]
[tex]5 - \sqrt{72} - (4 + 5 \sqrt{2} - ( \sqrt{98} - 20))[/tex]
[tex] = 5 - 6 \sqrt{2} - (4 + 5 \sqrt{2} - (7 \sqrt{2} - 20))
= 5 - 6 \sqrt{2} - (4 + 5 \sqrt{2} - 7 \sqrt{2} + 20)
= 5 - 6 \sqrt{2} - (24 - 2 \sqrt{2)}
= 5 - 6 \sqrt{2} - 24 + 2 \sqrt{2} \\ \\ = - 19 - 4 \sqrt{2} [/tex]
[tex] = - 19 - 4 \sqrt{2} [/tex]
[tex] |2 - \sqrt{7} | + |3 - \sqrt{7} |
= \sqrt{7} - 2 + 3 - \sqrt{7} [/tex]
[tex] = - 2 + 3[/tex]
[tex] = 1[/tex]
[tex]|3 \sqrt{2} | + \sqrt{( 1 + \sqrt{2})^{2} }
= 3 \sqrt{2} + 1 + \sqrt{2}
= 4 \sqrt{2 } + 1
[/tex]
[tex] \sqrt{(31 - \sqrt{3} )^{2} } + \sqrt({2} - 3 ) ^{2} [/tex]
[tex] = 31 - \sqrt{3} + 2 - \sqrt{3} [/tex]
[tex] = 33 - 2 \sqrt{3} [/tex]
