Zad.1 Wykonaj działanie: a) [latex] sqrt{121} - 2sqrt{162} + sqrt{200} [/latex] [latex]b) ( sqrt{128} + sqrt{40} )* sqrt{2} [/latex] c) [latex]( sqrt{2} - 3 sqrt{3} ^2[/latex] d) [latex]( sqrt{3} +2)(2 sqrt{3} -3)[/latex] Daję Naj! 

[latex]a) sqrt{121}-2sqrt{162}+sqrt{200}=11-2sqrt{81cdot2}+sqrt{100cdot2}\\=11-2cdot9sqrt2+10sqrt2=11-18sqrt2+10sqrt2=11-8sqrt2\\b) (sqrt{128}+sqrt{40})cdotsqrt2=sqrt{128cdot2}+sqrt{40cdot2}=sqrt{256}+sqrt{80}\\=16+sqrt{16cdot5}=16+4sqrt5\\c) (sqrt2-3sqrt3)^2=(sqrt2)^2-2cdot2sqrt2cdot3sqrt3+(3sqrt3)^2\\=2-12sqrt3+9cdot3=2-12sqrt6+27=29-12sqrt6[/latex] [latex]d) (sqrt3+2)(2sqrt3-3)=2sqrt{3cdot3}-3sqrt3+4sqrt3-6\\=2cdot3+sqrt3-6=6+sqrt3-6=sqrt3\\\©DRK[/latex]

√121-2√162+√200=11-2(9√2)+10√2=11-18√2+10√2= -18√2+11+10√2= -8√2+11 (√128+√40)*√2=(8√2+2√10)*√2=4√5+16 (√2-3√3)²= -6√6+29 (√3+2)(2√3-3)=√3