Объяснение:

1.

[tex]a)\ \sqrt[3]{25*2}*\sqrt[3]{4*5} =\sqrt[3]{5^2*2*2^2*2*5} =\sqrt[3]{5^3*2^3}= 5*2=10.\\b)\ \sqrt[4]{6+2\sqrt{5} }*\sqrt{\sqrt{5}-1} =\sqrt[4]{5+1+2\sqrt{5} }*\sqrt{\sqrt{5}-1} = \\ =\sqrt[4]{(\sqrt{5)^2} +2\sqrt{5}*1+1^2 }*\sqrt{\sqrt{5}-1} =\sqrt[4]{(\sqrt{5}+1)^2 } *\sqrt{\sqrt{5}-1 }=\\ =\sqrt{\sqrt{5}+1 }*\sqrt{\sqrt{5}-1 } =\sqrt{(\sqrt{5}+1)*(\sqrt{5}-1) }=\sqrt{(\sqrt{5})^2-1^2 } =\\ =\sqrt{5-1} =\sqrt{4} =2.[/tex]

2.

[tex]a)\ 3\sqrt[3]{4} \ \vee\ 4\sqrt[3]{2} \\\sqrt[3]{3^3*4}\ \vee\ \sqrt[3]{4^3*2}\\ \sqrt[3]{27*4} \ \vee\ \sqrt[3]{64*2} \\\sqrt[3]{108}\ < \ \sqrt[3]{128} .\\b)\ \sqrt[4]{5\sqrt{2} } \ \vee\ \sqrt[8]{51}\\ \sqrt[4]{\sqrt{5^2*2} }\ \vee\ \sqrt[4]{\sqrt{51} } \\ \sqrt[4]{\sqrt{25*2} } \ \vee\ \sqrt[4]{\sqrt{51} } \\\sqrt[4]{\sqrt{50} }\ < \ \sqrt[4]{\sqrt{51} }.[/tex]

3.

[tex]a)\ \sqrt[5]{a^3*\sqrt[4]{a^3} } =\sqrt[5]{a^3*a^{\frac{3}{4}} } =\sqrt[5]{a^{3+\frac{3}{4} }}=\sqrt[5]{a^{\frac{15}{4} } } =a^{\frac{15}{5*4}}=a^{\frac{3}{4}} =\sqrt[4]{a^3}}.\\ b)\ \sqrt[4]{a^6b^{13}}=\sqrt[4]{a^4*a^2*b^{12}*b} =ab^3\sqrt{a^2b}.[/tex]