2. Trục căn thức ở mẫu :
a) 6/(sqrt(3))
b) 8/(5sqrt(2))
c) 1/(sqrt(a))
d) (sqrt(3) - 3)/(sqrt(3) - 1)
e) (a - sqrt(a))/(sqrt(a) - 1)
g) (1 - z * sqrt(a) + a)/(1 - sqrt(a))
h) 3/(sqrt(5) - sqrt(2))
i) (sqrt(2) + 1)/(sqrt(2) - 1)
k) (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3))
l) (1 + sqrt(a ^ 3))/(1 + sqrt(a))
m) (1 - a * sqrt(a))/(1 - sqrt(a))
a: \(\dfrac{6}{\sqrt{3}}=\dfrac{6\sqrt{3}}{3}=2\sqrt{3}\)
b: \(\dfrac{8}{5\sqrt{2}}=\dfrac{8\sqrt{2}}{5\sqrt{2}\cdot\sqrt{2}}=\dfrac{8\sqrt{2}}{5\cdot2}=\dfrac{4\sqrt{2}}{5}\)
c: \(\dfrac{1}{\sqrt{a}}=\dfrac{\sqrt{a}}{a}\)
d: \(\dfrac{\sqrt{3}-3}{\sqrt{3}-1}=\dfrac{-\sqrt{3}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}=-\sqrt{3}\)
e: \(\dfrac{a-\sqrt{a}}{\sqrt{a}-1}=\dfrac{\sqrt[]{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}=\sqrt{a}\)
h: \(\dfrac{3}{\sqrt{5}-\sqrt{2}}=\dfrac{3\left(\sqrt{5}+\sqrt{2}\right)}{5-2}=\dfrac{3}{3}\cdot\left(\sqrt{5}+\sqrt{2}\right)\)
\(=\sqrt{5}+\sqrt{2}\)
i: \(\dfrac{\sqrt{2}+1}{\sqrt{2}-1}=\dfrac{\left(\sqrt{2}+1\right)^2}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}=3+2\sqrt{2}\)
k: \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)}\)
\(=\dfrac{8-2\sqrt{15}}{5-3}=\dfrac{2\left(4-\sqrt{15}\right)}{2}=4-\sqrt{15}\)
l: \(\dfrac{1+\sqrt[]{a^3}}{1+\sqrt{a}}=\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}\)
\(=\dfrac{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}+a\right)}{1+\sqrt{a}}=1-\sqrt{a}+a\)
m: \(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}\)
\(=\dfrac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}=1+\sqrt{a}+a\)
