Bài 2:
\(a.\left(5-a\right)\sqrt{\dfrac{8a}{a-5}}\\ a>5 \\= \sqrt{\dfrac{8a\left(5-a\right)^2}{a-5}}\\ =\sqrt{\dfrac{8a\left(a-5\right)^2}{a-5}}\\ =\sqrt{8a\left(a-5\right)}=\sqrt{8a^2-40}\\b.\left(x-7\right)\sqrt{\dfrac{\left(x+7\right)}{49-x^2}}\\ =\left(x-7\right)\sqrt{\dfrac{\left(x+7\right)}{\left(7-x\right)\left(x+7\right)}}\\ \left(x-7\right)\sqrt{\dfrac{1}{7-x}}\\ =\sqrt{\dfrac{\left(x-7\right)^2}{7-x}}=\sqrt{\dfrac{\left(7-x\right)^2}{7-x}}\\ =\sqrt{7-x}\\ c.\)
\(\dfrac{a}{b}\sqrt{\dfrac{b}{a}}\\ a,b>0 \\ =\sqrt{\dfrac{a^2b}{b^2a}}=\sqrt{\dfrac{a}{b}}\\ d.x\sqrt{\dfrac{6}{x}}\\ x>0\\ =\sqrt{\dfrac{6x^2}{x}}=\sqrt{6x}\)
Bài 3:
\(a.7\sqrt{2}=\sqrt{7^2.2}=\sqrt{98}\)
Vì \(\sqrt{98}>\sqrt{72}\Rightarrow7\sqrt{2}>\sqrt{72}\)
\(b.4\sqrt[]{3}=\sqrt{4^2.3}=\sqrt{48}\\ 3\sqrt{5}=\sqrt{3^2.5}=\sqrt{45}\)
vì: \(48>45\Rightarrow\sqrt{48}>\sqrt{45}\Rightarrow4\sqrt{3}>3\sqrt{5}\)
c.\(4\sqrt{7}=\sqrt{4^2.7}=\sqrt{112}\\ 5\sqrt{6}=\sqrt{5^2.6}=\sqrt{150}\)
Vì: \(112< 150\Rightarrow\sqrt{112}< \sqrt{150}\Rightarrow4\sqrt{7}< 5\sqrt{6}\)
d.\(\dfrac{1}{6}\sqrt{18}=\sqrt{\dfrac{18}{6^2}}=\sqrt{\dfrac{18}{36}}=\sqrt{\dfrac{1}{2}}\\ \dfrac{1}{2}\sqrt{2}=\sqrt{\dfrac{2}{4}}=\sqrt{\dfrac{1}{2}}\)
Vì: \(\dfrac{1}{2}=\dfrac{1}{2}\Rightarrow\sqrt{\dfrac{1}{2}}=\sqrt{\dfrac{1}{2}}\Rightarrow\dfrac{1}{6}\sqrt{15}=\dfrac{1}{2}\sqrt{2}\)
