Answer:
[tex]\dfrac{2x}{3y}\sqrt{3y}[/tex]
Step-by-step explanation:
When we simplify a radical, we want to remove any squares from under the radical. Often, we also want to eliminate any fractions under the radical.
Here, that means we need to multiply by the denominator so as to make it a perfect square, then remove the square from under the radical.
[tex]\sqrt{\dfrac{4x^2}{3y}}=\sqrt{\dfrac{(2x)^2(3y)}{(3y)(3y)}}=\sqrt{\dfrac{(2x)^2(3y)}{(3y)^2}}\\\\=\dfrac{2x}{3y}\sqrt{3y}[/tex]
