+) \(2\sqrt{4ab}-3\sqrt{\dfrac{a}{b}}+\dfrac{a\sqrt{a^2b}}{\sqrt{a}}\)
\(=2\sqrt{4ab}-3\sqrt{\dfrac{a}{b}}+a\sqrt{ab}\)
+) \(\sqrt{\left(2\sqrt{7}-6\right)^2}+\sqrt{53-20\sqrt{7}}\)
\(=\sqrt{\left(6-2\sqrt{7}\right)^2}+\sqrt{53-10\sqrt{28}}\)
\(=\sqrt{\left(6-2\sqrt{7}\right)^2}+\sqrt{\left(2\sqrt{7}\right)^2-2.2\sqrt{7}.5+5^2}\)
\(=\left|6-2\sqrt{7}\right|+\sqrt{\left(2\sqrt{7}-5\right)^2}\)
\(=6-2\sqrt{7}+2\sqrt{7}-5\left(Vì\left\{{}\begin{matrix}6>2\sqrt{7}\\2\sqrt{7}>5\end{matrix}\right.\right)\)
\(=1\)
\(2\sqrt{4ab}-3\sqrt{\dfrac{a}{b}}+a\dfrac{\sqrt{a^2b}}{\sqrt{a}}\)
\(=2\sqrt{2^2.ab}-3\sqrt{\dfrac{a}{b}}+a\dfrac{\sqrt{a^2b}}{\sqrt{a}}\)
\(=2.2\sqrt{ab}-3\sqrt{\dfrac{a}{b}}+a\dfrac{\left|a\right|\sqrt{b}}{\sqrt{a}}\)
\(=4\sqrt{ab}-3\sqrt{\dfrac{a}{b}}+a.\dfrac{a\sqrt{b}}{\sqrt{a}}\) (vì ab > 0 nên a > 0)
\(=4\sqrt{ab}-3\sqrt{\dfrac{a}{b}}+\left(\sqrt{a}\right)^2.\dfrac{a\sqrt{b}}{\sqrt{a}}\)
\(=4\sqrt{ab}-3\sqrt{\dfrac{a}{b}}+a\sqrt{a}.\sqrt{b}\)
\(=4\sqrt{ab}-3\sqrt{\dfrac{a}{b}}+a\sqrt{ab}\)
\(\sqrt{\left(2\sqrt{7}-6\right)^2}+\sqrt{53-20\sqrt{7}}\)
\(=\left|2\sqrt{7}-6\right|+\sqrt{25-2.5.2\sqrt{7}+28}\)
\(=6-2\sqrt{7}+\sqrt{\left(5-2\sqrt{7}\right)^2}\) (vì \(2\sqrt{7}-6< 0\))
\(=6-2\sqrt{7}+\left|5-2\sqrt{7}\right|\)
\(=6-2\sqrt{7}+2\sqrt{7}-5\) (vì \(5-2\sqrt{7}< 0\))
\(=1\)
