Help on simplifying radicals (square roots)

1) 4 / √32   ?

$$\boxed{\dfrac{4 }{ \sqrt{32} }} \\ \\
=\dfrac{\sqrt{16} }{ \sqrt{32}} \\ \\
=\sqrt{ \dfrac{16 }{ 32} } \\ \\
=\sqrt{ \dfrac{1 }{ 2} } \\ \\
=\dfrac{1}{\sqrt{2} } * \dfrac{\sqrt{2}}{\sqrt{2}}\\\\
\boxed{=\dfrac{\sqrt{2}}{2}}$$

1) 4 / sqrt(32) =

4 / sqrt(4*8) =

4 / [sqrt(4)*sqrt(8)]=

4 / [2*sqrt(8)] =

2/ sqrt(8) * [sqrt8/sqrt8] =

2sqrt8/8 =

sqrt8/4.

 

2) 5 / sqrt(48) = 

5 / sqrt(16*3) = 

5 / [sqrt(16)*sqrt(3)] =

5 / [4*sqrt(3)] =

5 / 4sqrt3 * [sqrt3 / sqrt3] =

5sqrt3 / 12.

 

3) 3sqrt5 / sqrt(25) =

3sqrt5 / 5.

 

4) 3sqrt24 / sqrt(2) =

3*sqrt(2)*sqrt(12) / sqrt(2) =

3sqrt(12).

4) 3√24 / √2   ?

 $$\boxed{\dfrac{3 *\sqrt{24} }{ \sqrt{2} }} \\ \\
=3 *\sqrt{ \dfrac{24 }{ 2} } \\ \\
=3 *\sqrt{ 12 } \\ \\
=3 *\sqrt{ 4*3} \\ \\
=3 *\underbrace{\sqrt{ 4}}_{2}*\sqrt{3} \\ \\
=3 *2*\sqrt{3} \\ \\
\boxed{=6\sqrt{3}}$$