trục căn thưc ơ mâũ:
a)\(\dfrac{5}{\sqrt{7}}\)
b)\(\dfrac{1}{\sqrt{3}-2}\)
c)\(\dfrac{3}{\sqrt{5}+\sqrt{3}}\)
d)\(\dfrac{7}{\sqrt{2}-\sqrt{7}}\)
e)\(\dfrac{ab}{\sqrt{a}-\sqrt{b}}\)
f) \(\dfrac{p-\sqrt{p}}{3\sqrt{p}-1}\)
Rút gọn :
a)\(\dfrac{3+\sqrt{3}}{\sqrt{3}+1}\)
b)\(\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\)
1) trục căn thức và khử mẩu
a) \(\dfrac{5}{\sqrt{7}}=\dfrac{5\sqrt{7}}{\sqrt{7}\sqrt{7}}=\dfrac{5\sqrt{7}}{7}\)
b) \(\dfrac{1}{\sqrt{3}-2}=\dfrac{1.\left(\sqrt{3}+2\right)}{\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)}=\dfrac{\sqrt{3}+2}{\left(\sqrt{3}\right)^2-2^2}=\dfrac{\left(\sqrt{3}+2\right)}{3-4}\)
\(=\dfrac{-\left(\sqrt{3}+2\right)}{4-3}=\dfrac{-\sqrt{3}-2}{1}=-\sqrt{3}-2\)
c) \(\dfrac{3}{\sqrt{5}+\sqrt{3}}=\dfrac{3\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{3\sqrt{5}-3\sqrt{3}}{\left(\sqrt{5}\right)^2-\left(\sqrt{3}\right)^2}\)
\(=\dfrac{3\sqrt{5}-3\sqrt{3}}{5-3}=\dfrac{3\sqrt{5}-3\sqrt{3}}{2}\)
d) \(\dfrac{7}{\sqrt{2}-\sqrt{7}}=\dfrac{7\left(\sqrt{7}+\sqrt{2}\right)}{\left(\sqrt{2}-\sqrt{7}\right)\left(\sqrt{7}+\sqrt{2}\right)}=\dfrac{-7\left(\sqrt{7}+\sqrt{2}\right)}{\left(\sqrt{7}-\sqrt{2}\right)\left(\sqrt{7}+\sqrt{2}\right)}\)
\(=\dfrac{-7\sqrt{7}-7\sqrt{2}}{\left(\sqrt{7}\right)^2-\left(\sqrt{2}\right)^2}=\dfrac{-7\sqrt{7}-7\sqrt{2}}{7-2}=\dfrac{-7\sqrt{7}-7\sqrt{2}}{5}\)
e) điều kiện \(a;b\ge0\)
\(\dfrac{ab}{\sqrt{a}-\sqrt{b}}=\dfrac{ab\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}=\dfrac{ab\sqrt{a}+ab\sqrt{b}}{\left(\sqrt{a}\right)^2-\left(\sqrt{b}\right)^2}\)
\(=\dfrac{ab\sqrt{a}+ab\sqrt{b}}{a-b}\)
f) câu này đề sai thì phải : đề phải là \(\dfrac{p-\sqrt{p}}{3\left(\sqrt{p}-1\right)}\) mới đúng (theo mk nghỉ )
2) rút gọn
a) \(\dfrac{3+\sqrt{3}}{\sqrt{3}+1}=\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}=\sqrt{3}\)
b) \(\dfrac{a-\sqrt{a}}{1-\sqrt{a}}=\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{1-\sqrt{a}}=\dfrac{-\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}=-\sqrt{a}\)