Bài 1:
a. \(\sqrt{\frac{25m^2}{49}}=\frac{\sqrt{25m^2}}{\sqrt{49}}=\frac{5m}{7}\)
b. \(\frac{\sqrt{192k}}{\sqrt{3k}}=\sqrt{\frac{192k}{3k}}=\sqrt{64}=8\)
Bài 2:
a. \(\frac{a+\sqrt{a}}{\sqrt{a}}=\frac{\left(\sqrt{a}\right)^2+\sqrt{a}}{\sqrt{a}}=\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}}=\sqrt{a}+1\)
b. \(\frac{\sqrt{a}-a}{\sqrt{a}-1}=\frac{\sqrt{a}-\left(\sqrt{a}\right)^2}{\sqrt{a}-1}=\frac{\sqrt{a}\left(1-\sqrt{a}\right)}{\sqrt{a}-1}=\frac{-\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}=-\sqrt{a}\)
c. \(\frac{a-b}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}\right)^2-\left(\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}=\sqrt{a}+\sqrt{b}\)