3\sqrt{5c}\sqrt{15^3}3√5c√153
=3\sqrt{5}\sqrt{15^3}\sqrt{c}=3√5√153√c Reason: (\sqrt{5c}=\sqrt{5}\sqrt{c}√5c=√5√c)
=3\cdot \15\sqrt{5}\sqrt{15}\sqrt{c}=3⋅15√5√15√c Reason: (\sqrt{15^3}=15\sqrt{15}√153=15√15)
=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{15}=3√5√c⋅5⋅3√15 Reason:(15=3\cdot \515=3⋅5)
=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{5\cdot \3}=3√5√c⋅5⋅3√5⋅3 Reason:(15=3\cdot \515=3⋅5)
=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{5}\sqrt{3}=3√5√c⋅5⋅3√5√3 Reason:(\sqrt[n]^{ab}=\sqrt[n]^{a}\sqrt[n]^{b}√nab=√na√nb)
=5\cdot \3^{\frac{5}{2}}\sqrt{5}\sqrt{5}\sqrt{c}=5⋅352√5√5√c Reason:(a^b\cdot \a^c=a^{b+c}ab⋅ac=ab+c)
=3^2\cdot \5^2\sqrt{3}\sqrt{c}=32⋅52√3√c Reason:(\:a^b\cdot \:a^c=a^{b+c}:ab⋅:ac=ab+c)
=225\sqrt{3}\sqrt{c}=225√3√c Refined answer