Odpowiedź:
zad. 1
a)
[tex]\sqrt{2} *\sqrt{6} *\sqrt{3} =\sqrt{2*6*3} =\sqrt{36} =6[/tex]
b)
[tex]\sqrt[3]{10} *\sqrt[3]{20} *\sqrt[3]{40} =\sqrt[3]{10*20*40}=\sqrt[3]{8000} =20[/tex]
c)
[tex]\sqrt{3} *\sqrt{8} :\sqrt{6} =\sqrt{3*8:6}=\sqrt{4} =2[/tex]
d)
[tex]\sqrt[3]{10} *\sqrt[3]{25} :\sqrt[3]{2} =\sqrt[3]{10*25:2}=\sqrt[3]{125} =5[/tex]
e)
[tex]\sqrt{30} *\sqrt{50} :\sqrt{15} =\sqrt{30*50:15} =\sqrt{100} =10[/tex]
zad. 2
a)
[tex]\sqrt{3} *\sqrt[3]{3} *\sqrt{12} *\sqrt[3]{9} =\sqrt{3*12} *\sqrt[3]{3*9} =\sqrt{36} *\sqrt[3]{27} =6*3=18[/tex]
b)
[tex]\sqrt[3]{5} *\sqrt{20} *\sqrt{5} *\sqrt[3]{25} =\sqrt[3]{5*25} *\sqrt{20*5} =\sqrt[3]{125} *\sqrt{100} =5*10=50[/tex]
c)
[tex]\sqrt[3]{4} *\sqrt{18} *\sqrt[3]{250} :\sqrt{2} =\sqrt[3]{4*250}*\sqrt{18:2} =\sqrt[3]{1000} *\sqrt{9} =10*3=30[/tex]
d)
[tex]\sqrt{45} *\sqrt[3]{24} :\sqrt{5} :\sqrt[3]{3} =\sqrt{45:5} *\sqrt[3]{24:3} =\sqrt{9} *\sqrt[3]{8} =3*2=6[/tex]
Szczegółowe wyjaśnienie:
