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√ [ 128 r^3 ]  =

√64 *  √2 *    √ r^2   *   √ r   =

8 * √2 * r   * √ r  =

8r √ [ 2r ]

8r sqrt 2r. 

Welcome.

Hope this helps a little bit, sorry I don't have too much time for explanation. (and I don't understand why latex does not work here)

\(\sqrt{128r^3}=\sqrt{64 \times 2 \times r^2 \times r }=\sqrt{64} \sqrt{r^2} \sqrt{2r}=8r\sqrt{2r}\)

Hope this helps!