Question

Is sqrt(25a^2/4) the same as sqrt(25a^2)/sqrt(4)?

Answer 1

$LHS\\ \\ =\sqrt { \frac { 25{ a }^{ 2 } }{ 4 } } \\ \\ ={ \left( \frac { 25{ a }^{ 2 } }{ 4 } \right) }^{ \frac { 1 }{ 2 } }$

$\\ \\ =\frac { { \left( 25{ a }^{ 2 } \right) }^{ \frac { 1 }{ 2 } } }{ { 4 }^{ \frac { 1 }{ 2 } } } \\ \\ =\frac { \sqrt { 25{ a }^{ 2 } } }{ \sqrt { 4 } } \\ \\ =RHS$

Answer 2

Yes, because $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt a}{\sqrt b}$