\(\sqrt{112}-7\sqrt{\dfrac{1}{7}}-14\sqrt{\dfrac{1}{28}}-\dfrac{21}{\sqrt{7}}=\sqrt{16.7}-\sqrt{49.\dfrac{1}{7}}-2.\sqrt{\dfrac{1}{4}.49.\dfrac{1}{7}}-\dfrac{3.7}{\sqrt{7}}\)
\(=4\sqrt{7}-\sqrt{7}-2.\dfrac{1}{2}\sqrt{7}-3\sqrt{7}=4\sqrt{7}-\sqrt{7}-\sqrt{7}-3\sqrt{7}=-\sqrt{7}\)
\(=\sqrt{4^2.7}-\sqrt{\dfrac{7^2}{7}}-\sqrt{\dfrac{14^2}{\text{28}}}-\sqrt{3^2.7}\)
\(=4\sqrt{7}-\sqrt{7}-\sqrt{7}-3\sqrt{7}\)
\(=\sqrt{7}\left(4-1-1-3\right)\)
\(=-\sqrt{7}\)
\(\sqrt{112}-7\sqrt{\dfrac{1}{7}}-14\sqrt{\dfrac{1}{28}}-\dfrac{21}{\sqrt{7}}\)
=\(4\sqrt{7}-\sqrt{7}-\sqrt{7}-\dfrac{21\sqrt{7}}{7}\)
=\(2\sqrt{7}-\dfrac{21\sqrt{7}}{7}\)
=\(\dfrac{14\sqrt{7}-21\sqrt{7}}{7}\)
=\(\dfrac{-7\sqrt{7}}{7}\)
=\(-\sqrt{7}\)
