1.√160*(√20-√180+√125-√45)+√96*(√27-√12+√48+√3)
[tex] \sqrt{160}= \sqrt{2*80}= \sqrt{2^{4}*2*5}= 4\sqrt{10} \\ \sqrt{20}= \sqrt{4*5}=2 \sqrt{5} \\ \sqrt{180}= \sqrt{2*90}=6 \sqrt{5} \\ \sqrt{125}= 5\sqrt{5} \\ \sqrt{45}=3 \sqrt{5} \\ \sqrt{96}=4 \sqrt{6} \\ \sqrt{27}=3 \sqrt{3} \\ \sqrt{12}=2 \sqrt{3} \\ \sqrt{48}=4 \sqrt{3} \\ [/tex]
[tex]4 \sqrt{10}(2 \sqrt{5}-6 \sqrt{5}+5 \sqrt{5}-3 \sqrt{5})+ 4 \sqrt{6}(3 \sqrt{3}-2 \sqrt{3}+4 \sqrt{3}+ \sqrt{3} \\ =4 \sqrt{10}(7 \sqrt{5}-9 \sqrt{5})+4 \sqrt{6}(6 \sqrt{3}) \\ =4 \sqrt{10} *(-2 \sqrt{5})+24 \sqrt{18}=-8 \sqrt{50}+24 \sqrt{18} \\= 24 \sqrt{6*3}-8 \sqrt{2*5^{2} =74 \sqrt{2} }-40 \sqrt{2}=34 \sqrt{2} [/tex]
b)
√27*(√125-√45+√80-√500)-√20*(√75+√27-√108+√12)
[tex]3 \sqrt{3}(5 \sqrt{5}-3 \sqrt{5}+4 \sqrt{5}-10 \sqrt{5})-2 \sqrt{5}(5 \sqrt{3}+3 \sqrt{3}-6 \sqrt{3} +2 \sqrt{3} \\ 3 \sqrt{3}(-4 \sqrt{5})-2 \sqrt{5}(4 \sqrt{3})= \\ -12 \sqrt{15}-10 \sqrt{15}=-22 \sqrt{15} [/tex]
