Answer:
(2√(3m))/3
Step-by-step explanation:
You want the simplified form of ...
[tex]\dfrac{\sqrt{8m^2}}{\sqrt{6m}}[/tex]
Rules of radicals
The relevant rules of radicals are ...
[tex]\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}\\\\\sqrt{a^2b}=|a|\sqrt{b}[/tex]
Application
Applying these rules to the given expression, we can simplify it to ...
[tex]\dfrac{\sqrt{8m^2}}{\sqrt{6m}}=\sqrt{\dfrac{8m^2}{6m}}=\sqrt{\dfrac{4}{3}m}[/tex]
We want the denominator outside the radical. This is accomplished by multiplying the numerator and denominator of the fraction by 3 to make the denominator a perfect square.
[tex]=\sqrt{\dfrac{2^2\cdot3}{3^2}m}=\sqrt{\left(\dfrac{2}{3}\right)^23m}=\dfrac{2}{3}\sqrt{3m}=\boxed{\dfrac{2\sqrt{3m}}{3}}[/tex]
