Given:
[tex]\sqrt{\frac{6}{x}}\cdot\sqrt{\frac{x^2}{24}}[/tex]
Simplify:
[tex]=\sqrt{\frac{6}{x}}\cdot\frac{\sqrt{x^2}}{\sqrt{24}}=\sqrt{\frac{6}{x}}\cdot\frac{x}{2\sqrt{6}}[/tex]
Apply the properties of fractions:
[tex]=\frac{\sqrt{\frac{6}{x}}x}{2\sqrt{6}}[/tex]
Simplify:
[tex]=\frac{\frac{\sqrt{6}}{\sqrt{x}}x}{2\sqrt{6}}=\frac{\sqrt{6}\sqrt{x}}{2\sqrt{6}}[/tex]
Eliminate common terms:
[tex]=\frac{\sqrt{x}}{2}[/tex]
Answer:
[tex]\frac{\sqrt{x}}{2}[/tex]
