Question

a)√48·(2√75-√27+2√27)-√48·√12
b)√243·√147-2√3·7√3+3√8(5√72+6√128
c)(5√6-√96):√3-√48·(√24+4√6)
d)(3√14-√350):√7-(2√486-√294):√3
e){4√2+4·[3√3+3·(3√2-√3)]}
f)30√180+4√5·{18√2-3√5·[2√40-3(√40-√5)]}

Answer 1

$a). \sqrt{48} (2 \sqrt{75} - \sqrt{27} +2 \sqrt{27} )- \sqrt{48} * \sqrt{12} = \\ =4 \sqrt{3} (2*5 \sqrt{3} -3 \sqrt{3} +2*3 \sqrt{3} )-4 \sqrt{3} *2 \sqrt{3} = \\ =4 \sqrt{3} (10 \sqrt{3} -3 \sqrt{3} +6 \sqrt{3} )-24=120-36+72-24=132 \\ b). \sqrt{243} * \sqrt{147} -2 \sqrt{3} *7 \sqrt{3} +3 \sqrt{8} (5 \sqrt{72} +6 \sqrt{128} )= \\ =9 \sqrt{3} *7 \sqrt{3} -42+3*2 \sqrt{2} (5*6 \sqrt{2} +6*8 \sqrt{2} )= \\ =189-42+6 \sqrt{2} (30 \sqrt{2} +48 \sqrt{2} )=189-42+6 \sqrt{2} *78 \sqrt{2} = \\ =189-42+936=1083$
$c).(5 \sqrt{6} - \sqrt{96} ): \sqrt{3} - \sqrt{48} ( \sqrt{24} +4 \sqrt{6} )= \\ =(5 \sqrt{6} -4 \sqrt{6} ): \sqrt{3} -4 \sqrt{3} (2 \sqrt{6} +4 \sqrt{6} )= \\ = \sqrt{6} : \sqrt{3} -4 \sqrt{3} *6 \sqrt{6} = \sqrt{2} -24 \sqrt{18} = \sqrt{2} -24*3 \sqrt{2} = \\ = \sqrt{2} -72 \sqrt{2} =-71 \sqrt{2}$
$d).(3 \sqrt{14} - \sqrt{350} ): \sqrt{7} -(2 \sqrt{486} - \sqrt{294} ): \sqrt{3} = \\ =(3 \sqrt{14} -5 \sqrt{14} ): \sqrt{7} -(2*9 \sqrt{6} -7 \sqrt{6} ): \sqrt{3}= \\ =-2 \sqrt{14} : \sqrt{7} -(18 \sqrt{6} -7 \sqrt{6} ): \sqrt{3} =-2 \sqrt{2} -11 \sqrt{6} : \sqrt{3} = \\ =-2 \sqrt{2} -11 \sqrt{2} =-13 \sqrt{2}$
$e). \left \{ 4 \sqrt{2} +4[3 \sqrt{3} +3(3 \sqrt{2} - \sqrt{3} )] \left \}=$
$[4 \sqrt{2} +4(3 \sqrt{3} +9 \sqrt{2} -3 \sqrt{3} )]= 4 \sqrt{2} +4*9 \sqrt{2} = \\ =4 \sqrt{2} +36 \sqrt{2} =40 \sqrt{2}$
$f).30 \sqrt{180} +4 \sqrt{5} \left \{18 \sqrt{2} -3 \sqrt{5} [2 \sqrt{40} -3( \sqrt{40} - \sqrt{5} )] \left \}=$
$=30 \sqrt{180} +4 \sqrt{5} [ 18 \sqrt{2} -3 \sqrt{5} (2 \sqrt{40} -3 \sqrt{40} +3 \sqrt{5} )]= \\ =30 \sqrt{180} +4 \sqrt{5} [18 \sqrt{2} -3 \sqrt{5} (2*2 \sqrt{10} -3*2 \sqrt{10} +3 \sqrt{5} )]= \\ =30 \sqrt{180}+4 \sqrt{5} [18 \sqrt{2} -3 \sqrt{5} (4 \sqrt{10} -6 \sqrt{10} +3 \sqrt{5} )]= \\ =30 \sqrt{180} +4 \sqrt{5} [18 \sqrt{2} -3 \sqrt{5} (-2 \sqrt{10} +3 \sqrt{5} )]= \\ =30 \sqrt{180}+4 \sqrt{5} (18 \sqrt{2} +6 \sqrt{50} +3 \sqrt{5} )=$
$=30 \sqrt{180} +4 \sqrt{5} (18 \sqrt{2} +6*5 \sqrt{2} + 3 \sqrt{5} )= \\ =30 \sqrt{180} +4 \sqrt{5} (18 \sqrt{2} +30 \sqrt{2} +3 \sqrt{5} )= \\ =30 \sqrt{180}+4 \sqrt{5} ( 48 \sqrt{2} +3 \sqrt{5} )=30 \sqrt{180} +192 \sqrt{10} +60= \\ =30*6 \sqrt{5} +192 \sqrt{10} +60=180 \sqrt{5} +192 \sqrt{10} +60$