Question

Задания во вкладках-.....

Answer 1

$\sqrt{47-4 \sqrt{33} } + \sqrt{47+4 \sqrt{33} } =A>0 \\\ A^2=47-4 \sqrt{33} +47+4 \sqrt{33} +2 \sqrt{47-4 \sqrt{33} } \sqrt{47+4 \sqrt{33} }= \\\ =94+2 \sqrt{(47-4 \sqrt{33})(47+4 \sqrt{33} )}=94+2 \sqrt{2209-528}= \\\ =94+2 \sqrt{1681}=94+82=176 \\\ A= \sqrt{176} =4 \sqrt{11}$

$\sqrt[3]{5 \sqrt{2}- 7} \cdot \sqrt{3+2 \sqrt{2} } = \sqrt[6]{(5 \sqrt{2}- 7)^2} \cdot \sqrt[6]{(3+2 \sqrt{2} )^3} = \\\ =\sqrt[6]{(5 \sqrt{2}- 7)^2(3+2 \sqrt{2} )^3} = \\\ =\sqrt[6]{(50+49-70 \sqrt{2})(27+54 \sqrt{2}+72+16 \sqrt{2} )} = \\\ =\sqrt[6]{(99-70 \sqrt{2})(99+70 \sqrt{2} )} =\sqrt[6]{99^2-(70 \sqrt{2})^2 } = \\\ =\sqrt[6]{9801-9800 } =1$