An algebra problem by Gourab Roy

$\sqrt{\frac{16}{9}}+\sqrt{\frac{25}{9}}=\frac{4}{3}+\frac{5}{3}=\frac{9}{3}=\boxed{3}$

$\sqrt {\dfrac{16}{9}} + \sqrt {\dfrac{25}{9}}$

$\Rightarrow$ $\dfrac{4}{3}$ $+$ $\dfrac{5}{3}$ $=$ $\dfrac{9}{3}$ $= 3$

Its very easy. Root 16/9 gives 4/3 and root 25/9 gives us 5/3. On adding them we get 9/3. Then by reducing the result to lowest terms its 3.