Question

Bài 1: Tính giá trị biểu thức:

a) \(\dfrac{3}{\sqrt{6}-\sqrt{3}}+\dfrac{4}{\sqrt{7}+\sqrt{3}}\)

b) \(\dfrac{6}{3\sqrt{2}+2\sqrt{3}}\)

c) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\dfrac{\sqrt{5}+1}{\sqrt{5}-1}\)

d) \(\dfrac{\sqrt{2}}{2\sqrt{3}+4\sqrt{2}}\)

e) \(\dfrac{6}{\sqrt{2}-\sqrt{3}+3}\)

f) \(\dfrac{1}{\sqrt{10}+\sqrt{15}+\sqrt{14}+\sqrt{21}}\)

g) \(\dfrac{\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}}{\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}}\)

h) \(\dfrac{2\sqrt{30}}{\sqrt{5}+\sqrt{6}+\sqrt{7}}\)

i) \(\sqrt{24}+6\sqrt{\dfrac{2}{3}}+\dfrac{10}{\sqrt{6}-1}\)

Answer 1

a: \(=\sqrt{6}+\sqrt{3}+\sqrt{7}-\sqrt{3}=\sqrt{7}+\sqrt{6}\)

b: \(=\dfrac{6}{\sqrt{6}\left(\sqrt{3}+\sqrt{2}\right)}=\dfrac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}=\sqrt{18}-2\sqrt{3}\)

c: \(=\dfrac{8-2\sqrt{15}+8+2\sqrt{15}}{2}-\dfrac{6+2\sqrt{5}}{4}\)

\(=\dfrac{32-6-2\sqrt{5}}{4}=\dfrac{13-\sqrt{5}}{2}\)