Răspuns :
[tex]\displaystyle a).4 \sqrt{90} - \sqrt{10} -\left(3 \sqrt{160} -5 \sqrt{40} \right)=\\ \\ =4 \cdot 3 \sqrt{10} - \sqrt{10}- \left(3 \cdot 4 \sqrt{10} -5 \cdot 2 \sqrt{10} \right)=\\ \\ =12 \sqrt{10} - \sqrt{10} - \left(12 \sqrt{10} -10 \sqrt{10} \right)=12 \sqrt{10} - \sqrt{10} -2 \sqrt{10} = \\ \\ =11 \sqrt{10} -2 \sqrt{10} =9 \sqrt{10} [/tex]
[tex]\displaystyle b).9 \sqrt{27} +5 \sqrt{24} -\left(-2 \sqrt{96} - \sqrt{150} +3 \sqrt{243} \right)= \\ \\ =9 \cdot 3 \sqrt{3} +5 \cdot 2 \sqrt{6} -\left(-2 \cdot 4 \sqrt{6} -5 \sqrt{6} +3 \cdot 9 \sqrt{3} \right)= \\ \\ =27 \sqrt{3} +10 \sqrt{6} -\left(-8 \sqrt{6} -5 \sqrt{6} +27 \sqrt{3} \right)= \\ \\ =27 \sqrt{3} +10 \sqrt{6} - \left(-13 \sqrt{6} +27 \sqrt{3} \right)=\\ \\ =27 \sqrt{3} +10 \sqrt{6} +13 \sqrt{6} -27 \sqrt{3} =23 \sqrt{6} [/tex]
[tex]\displaystyle c).4 \sqrt{84} -10 \sqrt{189} -12 \sqrt{1029} +2 \sqrt{525} = \\ \\ =4 \cdot 2 \sqrt{21} -10 \cdot 3 \sqrt{21} -12 \cdot 7 \sqrt{21} +2 \cdot 5 \sqrt{21} = \\ \\ =8 \sqrt{21} -30 \sqrt{21} -84 \sqrt{21} +10 \sqrt{21} =-96 \sqrt{21} [/tex]
[tex]\displaystyle d).5 \sqrt{243} +2 \sqrt{48} -\left(8 \sqrt{300} -6 \sqrt{363} \right)= \\ \\ =5 \cdot 9 \sqrt{3} +2 \cdot 4 \sqrt{3} - \left(8 \cdot 10 \sqrt{3} -6 \cdot 11 \sqrt{3} \right)= \\ \\ =45 \sqrt{3} +8 \sqrt{3} -\left(80 \sqrt{3} -66 \sqrt{3} \right)=45 \sqrt{3} +8 \sqrt{3} -14 \sqrt{3} = \\ \\ =53 \sqrt{3} -14 \sqrt{3} =39 \sqrt{3} [/tex]
[tex]\displaystyle b).9 \sqrt{27} +5 \sqrt{24} -\left(-2 \sqrt{96} - \sqrt{150} +3 \sqrt{243} \right)= \\ \\ =9 \cdot 3 \sqrt{3} +5 \cdot 2 \sqrt{6} -\left(-2 \cdot 4 \sqrt{6} -5 \sqrt{6} +3 \cdot 9 \sqrt{3} \right)= \\ \\ =27 \sqrt{3} +10 \sqrt{6} -\left(-8 \sqrt{6} -5 \sqrt{6} +27 \sqrt{3} \right)= \\ \\ =27 \sqrt{3} +10 \sqrt{6} - \left(-13 \sqrt{6} +27 \sqrt{3} \right)=\\ \\ =27 \sqrt{3} +10 \sqrt{6} +13 \sqrt{6} -27 \sqrt{3} =23 \sqrt{6} [/tex]
[tex]\displaystyle c).4 \sqrt{84} -10 \sqrt{189} -12 \sqrt{1029} +2 \sqrt{525} = \\ \\ =4 \cdot 2 \sqrt{21} -10 \cdot 3 \sqrt{21} -12 \cdot 7 \sqrt{21} +2 \cdot 5 \sqrt{21} = \\ \\ =8 \sqrt{21} -30 \sqrt{21} -84 \sqrt{21} +10 \sqrt{21} =-96 \sqrt{21} [/tex]
[tex]\displaystyle d).5 \sqrt{243} +2 \sqrt{48} -\left(8 \sqrt{300} -6 \sqrt{363} \right)= \\ \\ =5 \cdot 9 \sqrt{3} +2 \cdot 4 \sqrt{3} - \left(8 \cdot 10 \sqrt{3} -6 \cdot 11 \sqrt{3} \right)= \\ \\ =45 \sqrt{3} +8 \sqrt{3} -\left(80 \sqrt{3} -66 \sqrt{3} \right)=45 \sqrt{3} +8 \sqrt{3} -14 \sqrt{3} = \\ \\ =53 \sqrt{3} -14 \sqrt{3} =39 \sqrt{3} [/tex]
