Question

Преобразование выражений

Answer 1

$sqrt[3]{18} cdot sqrt[3]{-12} = sqrt[3]{18 cdot(-12)} =-sqrt[3]{2cdot9 cdot4cdot3} =-sqrt[3]{2^3cdot3^3} =-2cdot3=-6\\ 0.5cdot sqrt[3]{ frac{120}{15} } =0.5cdot sqrt[3]{8 } =0.5cdot sqrt[3]{2^3 } =0.5cdot2=1\\ 4cdot sqrt[3]{ frac{540}{20} } =4cdot sqrt[3]{27} =4cdot sqrt[3]{3^3} = 4cdot 3 = 12\\ sqrt[3]{36cdot24cdot54} = sqrt[3]{9cdot4cdot3cdot8cdot2cdot27} = sqrt[3]{3^2cdot2^2cdot3cdot2^3cdot2cdot3^3} = sqrt[3]{3^6cdot2^6} =\ =3^2cdot2^2=9cdot4=12$

$sqrt[3]{12cdot32cdot36}= sqrt[3]{4cdot3cdot32cdot9cdot4}= sqrt[3]{2^2cdot3cdot2^5cdot3^2cdot2^2}= sqrt[3]{2^9cdot3^3} =\ =2^3cdot3=8cdot3=24\\ frac{20 sqrt[3]{3} }{ sqrt[3]{375} } =20 sqrt[3]{ frac{3}{375} } =20 sqrt[3]{ frac{1}{125} } = frac{20}{ sqrt[3]{5^3} } = frac{20}{5}=4\\ frac{ sqrt[3]{320} }{4 sqrt[3]{5} } = frac{1}{4} sqrt[3]{ frac{320}{5} } = frac{1}{4} sqrt[3]{ 64 } =frac{1}{4} sqrt[3]{ 2^6 } = frac{2^2}{4} =1$

$(2 sqrt[4]{25} )^2=(2 sqrt[4]{5^2} )^2=2^2cdotsqrt[4]{5^4}=4cdot5=20\\ (3cdot sqrt[3]{64} )^2=3^2cdot (sqrt[3]{2^6})^2=9cdot2^4=9cdot16=144\\ sqrt[3]{54} cdot sqrt[3]{4} - sqrt{2}cdot sqrt{8} = sqrt[3]{54cdot4} - sqrt{2cdot8} =sqrt[3]{27cdot2cdot2^2} - sqrt{2cdot2^3} =\ sqrt[3]{3^3cdot2^3} - sqrt{2^4} =6-2^2=6-4=2$

$sqrt[3]{16} cdot sqrt[3]{4} -2 sqrt[3]{27} = sqrt[3]{4^3} -2 sqrt[3]{3^3} =4-2cdot3=4-6=-2\\ sqrt[3]{25cdot60cdot18} = sqrt[3]{5^2cdot5cdot4cdot3cdot9cdot2} = sqrt[3]{5^3cdot2^3cdot3^3} =5cdot2cdot3=30\\ frac{ sqrt{22}cdot sqrt{18} }{3 sqrt{11} } = frac{1}{3} sqrt{ frac{396}{11} } =frac{1}{3} sqrt{36} =frac{1}{3} sqrt{6^2} =2$

$frac{ sqrt{21}cdot sqrt{12} }{2 sqrt{7} } = frac{1}{2} sqrt{ frac{252}{7} } =frac{1}{2} sqrt{36} =frac{1}{2} sqrt{6^2} =3\\ frac{ sqrt{6}cdot sqrt{30} }{2 sqrt{5} } = frac{1}{2} sqrt{ frac{180}{5} } =frac{1}{2} sqrt{36} =frac{1}{2} sqrt{6^2} =3$