$\sqrt{108}\ast \sqrt{3}=\sqrt{108\ast 3}=\sqrt{36\ast 3\ast 3}=\sqrt{36}\ast \sqrt{3^2}=6\ast 3=1$

$\sqrt{52}\ast \sqrt{13}=\sqrt{52\ast 13}=\sqrt{4\ast 13\ast 13}=\sqrt{4}\ast \sqrt{{13}^2}=2\ast 13=26$

$\sqrt{160}\ast \sqrt{250}=\sqrt{160\ast 250}=\sqrt{16\ast 10\ast 25\ast 10}=\sqrt{16}\ast \sqrt{25}\ast \sqrt{{10}^2}=4\ast 5\ast 10=20\ast 10=200$

$\sqrt{0,4}\ast \sqrt{4,9}=\sqrt{0,4\ast 4,9}=\sqrt{4\ast 49\ast 0,01}=\sqrt{4}\ast \sqrt{49}\ast \sqrt{0,01}=2\ast 7\ast 0,1=14\ast 0,1=1,4$

$\frac{\sqrt{288}}{\sqrt{2}}=\sqrt{\frac{288}{2}}=\sqrt{144}=12$

$\frac{\sqrt{90}}{\sqrt{0,225}}=\sqrt{\frac{90}{0,225}}=\sqrt{\frac{9}{0,0225}}=\frac{\sqrt{9}}{\sqrt{0,0225}}=\frac{3}{0,15}=\frac{300}{15}=20$