Question

Помогите решить примеры: 1) 2) 3)

Answer 1

$\sqrt[4]{24\cdot 54} = \sqrt[4]{4\cdot6\cdot 6\cdot9} = \sqrt[4]{4\cdot9\cdot 36} =\sqrt{2\cdot3\cdot 6} =\sqrt{6\cdot 6} =6$

$\dfrac{ \sqrt[3]{1152} \cdot \sqrt[3]{12} }{8} = \dfrac{ \sqrt[3]{1152\cdot 12} }{8} = \dfrac{ \sqrt[3]{8\cdot 144\cdot 12} }{8} = \dfrac{ \sqrt[3]{2^3\cdot 12^3} }{8} =\dfrac{ 2\cdot 12 }{8}=3$

$(5 \sqrt[3]{6 \sqrt{32}} -2 \sqrt[3]{75 \sqrt{50} })^5 = (5 \sqrt[3]{6\cdot4 \sqrt{2} } -2 \sqrt[3]{75 \cdot 5 \sqrt{2} })^5 = \\\ =(5 \sqrt[3]{24\sqrt{2} } -2 \sqrt[3]{375 \sqrt{2} })^5 =(5 \sqrt[3]{8\cdot 3\sqrt{2} } -2 \sqrt[3]{125\cdot3 \sqrt{2} })^5 = \\\ =(5 \cdot 2\sqrt[3]{3\sqrt{2} } -2\cdot5 \sqrt[3]{3 \sqrt{2} })^5 = (10\sqrt[3]{3\sqrt{2} } -10 \sqrt[3]{3 \sqrt{2} })^5 =0^5=0$