$a)5\sqrt{5}=\sqrt{5^2}\cdot \sqrt{5}=\sqrt{25}\cdot \sqrt{5}=\sqrt{125}$

$b)7\sqrt{2}=\sqrt{7^2}\cdot \sqrt{2}=\sqrt{49}\cdot \sqrt{2}=\sqrt{98}$

$c)5\sqrt{7}=\sqrt{5^2}\cdot \sqrt{7}=\sqrt{25}\cdot \sqrt{7}=\sqrt{175}$ $c)5\sqrt{7}=\sqrt{5^2}\cdot \sqrt{7}=\sqrt{25}\cdot \sqrt{7}=\sqrt{175}$

$d)0,4\sqrt{3}=\sqrt{{0,4}^2}\cdot \sqrt{3}=\sqrt{0,16}\cdot \sqrt{3}=\sqrt{0,16\cdot 3}=\sqrt{0,48}$

$e)\frac{1}{2}\cdot \sqrt{8}=\sqrt{{\left(\frac{1}{2}\right)}^2}\cdot \sqrt{8}=\sqrt{\frac{1}{4}}\cdot \sqrt{8}=\sqrt{\frac{1}{4}\cdot 8}=\sqrt{\frac{8}{4}}=\sqrt{2}$

$f)\frac{1}{3}\cdot \sqrt{18}=\sqrt{{\left(\frac{1}{3}\right)}^2}\cdot \sqrt{18}=\sqrt{\frac{1}{9}}\cdot \sqrt{18}=\sqrt{\frac{1}{{\sout{9}}^1}\cdot {\sout{18}}^2}=\sqrt{2}$

$g)3\sqrt[3]{4}=\sqrt[3]{3^3}\cdot \sqrt[3]{4}=\sqrt[3]{27}\cdot \sqrt[3]{4}=\sqrt[3]{27\cdot 4}=\sqrt[3]{108}$

$h)4\sqrt[3]{3}=\sqrt[3]{4^3}\cdot \sqrt[3]{3}=\sqrt[3]{64}\cdot \sqrt[3]{3}=\sqrt[3]{64\cdot 3}=\sqrt[3]{192}$

$i)10\sqrt[3]{-1,1}=\sqrt[3]{{10}^3}\cdot \sqrt[3]{-1,1}=\sqrt[3]{1000}\cdot \sqrt[3]{-1,1}=\sqrt[3]{1000\cdot \left(-1,1\right)}=\sqrt[3]{-1100}$

$j)0,5\sqrt[3]{56}=\frac{1}{2}\sqrt[3]{56}=\sqrt[3]{{0,5}^3}\cdot \sqrt[3]{56}=\sqrt[3]{{\left(0,5\right)}^3\cdot 56}=\sqrt[3]{{\left(\frac{1}{2}\right)}^3\cdot 56}=$

$=\sqrt[3]{\frac{1}{{\sout{8}}^1}\cdot {\sout{56}}^7}=\sqrt[3]{7}$