$a\sqrt{3}=\sqrt{a^2}\ast \sqrt{3}=\sqrt{3a^2}$

$b\sqrt{-b}=\sqrt{b^2}\ast \sqrt{-b}=\sqrt{b^2\ast (-b)}=\sqrt{-b^3}$

$c\sqrt{c^5}=\sqrt{c^2}\ast \sqrt{c^5}=\sqrt{c^2\ast c^5}=\sqrt{c^7}$

$m\sqrt{n}=\sqrt{m^2}\ast \sqrt{n}=\sqrt{m^{2}n}$, если m ≥ 0

$x{y}^2\sqrt{xy}=-\sqrt{x^2}\ast \sqrt{(y^2{)}^2}\ast \sqrt{xy}=-\sqrt{x^2{y}^4\ast xy}=-\sqrt{x^3{y}^5}$, если x ≤ 0

$2p\sqrt{\frac{p}{2}}=\sqrt{(2p{)}^2}\ast \sqrt{\frac{p}{2}}=\sqrt{4p^2\ast (\frac{p}{2})}=\sqrt{2p^2\ast p}=\sqrt{2p^3}$

$2p\sqrt{-\frac{p}{2}}=-\sqrt{(2p{)}^2}\ast \sqrt{-\frac{p}{2}}=-\sqrt{4p^2\ast (-\frac{p}{2})}=-\sqrt{2p^2\ast (-p)}=-\sqrt{-2p^3}$

$a{b}^2\sqrt{\frac{a}{b}}=\sqrt{(a{b}^2{)}^2}\ast \sqrt{\frac{a}{b}}=\sqrt{a^2{b}^4\ast \frac{a}{b}}=\sqrt{a^2{b}^3\ast a}=\sqrt{a^3{b}^3}$, если a ≥ 0