$\sqrt{125}\cdot \sqrt{5}=\sqrt{125\cdot 5}=\sqrt{25\cdot 5\cdot 5}=\sqrt{25\cdot 25}=25$

$\sqrt{12}\cdot \sqrt{27}=\sqrt{12\cdot 27}=\sqrt{3\cdot 4\cdot 9\cdot 3}=\sqrt{3\cdot 3\cdot 4\cdot 9}=\sqrt{9\cdot 36}=\sqrt{9}\cdot \sqrt{36}=3\cdot 6=18$

$\sqrt{0,1}\cdot \sqrt{10}=\sqrt{0,1\cdot 10}=\sqrt{1}=1$

$\sqrt{\frac{3}{4}}\cdot \sqrt{12}=\sqrt{\frac{3}{{\sout{4}}^1}\cdot {\sout{12}}^3}=\sqrt{9}=3$

$\sqrt{\frac{2}{3}}\cdot \sqrt{\frac{6}{25}}=\sqrt{\frac{2}{{\sout{3}}^1}\cdot \frac{{\sout{6}}^2}{25}}=\sqrt{\frac{4}{25}}=\frac{\sqrt{4}}{\sqrt{25}}=\frac{2}{5}=0,4$

$\sqrt[3]{9}\cdot \sqrt[3]{3}=\sqrt[3]{27}=3$

 

$\sqrt{125}\cdot \sqrt{5}$	$\sqrt{12}\cdot \sqrt{27}$	$\sqrt{0,1}\cdot \sqrt{10}$	$\sqrt{\frac{3}{4}}\cdot \sqrt{12}$	$\sqrt{\frac{2}{3}}\cdot \sqrt{\frac{6}{25}}$	$\sqrt[3]{9}\cdot \sqrt[3]{3}$
$25$	$18$	$1$	$3$	$0,4$	$3$