Question

1. Trục căn thức ở mẫu

a, \(\dfrac{5\sqrt{2}}{\sqrt{5}+\sqrt{3}}\)

b, \(\dfrac{\sqrt{5}+1}{2\sqrt{5}-4}\)

c, \(\dfrac{3}{2\sqrt{2}-\sqrt{5}}\)

d, \(\dfrac{1}{2+\sqrt{3}-\sqrt{6}}\)

giúp mk vs ạ mk tik cho

giải cụ thể cùng mk

Answer 1

\(a=\frac{5\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\frac{5\sqrt{10}-5\sqrt{6}}{2}\)

\(b=\frac{\left(\sqrt{5}+1\right)\left(2\sqrt{5}-4\right)}{\left(2\sqrt{5}-4\right)\left(2\sqrt{5}+4\right)}=\frac{6-2\sqrt{5}}{4}=\frac{3-\sqrt{5}}{2}\)

\(c=\frac{3\left(2\sqrt{2}+\sqrt{5}\right)}{\left(2\sqrt{2}-\sqrt{5}\right)\left(2\sqrt{2}+\sqrt{5}\right)}=\frac{6\sqrt{2}+3\sqrt{5}}{3}=2\sqrt{2}+\sqrt{5}\)

\(d=\frac{2+\sqrt{3}+\sqrt{6}}{\left(2+\sqrt{3}-\sqrt{6}\right)\left(2+\sqrt{3}+\sqrt{6}\right)}=\frac{2+\sqrt{3}+\sqrt{6}}{4\sqrt{3}+1}=\frac{\left(2+\sqrt{3}+\sqrt{6}\right)\left(4\sqrt{3}-1\right)}{\left(4\sqrt{3}-1\right)\left(4\sqrt{3}+1\right)}\)

\(=\frac{10+7\sqrt{3}+12\sqrt{2}-\sqrt{6}}{47}\)