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

\(=\sqrt{\dfrac{\left(\sqrt{3}-\sqrt{2}\right)^2}{3-2}}+\sqrt{\dfrac{\left(\sqrt{3}+\sqrt{2}\right)^2}{3-2}}\)

\(=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)

\(=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}=2\sqrt{3}\)

\(\sqrt{2-\sqrt{3}}=\frac{\sqrt{2}.\sqrt{2-\sqrt{3}}}{\sqrt{2}}=\frac{\sqrt{2.\left(2-\sqrt{3}\right)}}{\sqrt{2}}=\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\frac{\sqrt{3-2\sqrt{3}+1}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}}=\frac{\left|\sqrt{3}-1\right|}{\sqrt{2}}=\frac{\sqrt{3}-1}{\sqrt{2}}=\frac{\sqrt{2}.\left(\sqrt{3}-1\right)}{\sqrt{2}.\sqrt{2}}=\frac{\sqrt{2}.\sqrt{3}-\sqrt{2}.1}{\sqrt{2.2}}=\frac{\sqrt{2.3}-\sqrt{2}}{\sqrt{4}}=\frac{\sqrt{6}-\sqrt{2}}{2}\)

\(A=2\sqrt{3}+\sqrt{\left(2+\sqrt{3}\right)^2}\\ =2\sqrt{3}+\left|2+\sqrt{3}\right|\\ =2\sqrt{3}+2+\sqrt{3}\\ =3\sqrt{3}+2\)

Sửa đề `->sqrt{7+4sqrt3}`

`=sqrt{7+4sqrt3}`

`=sqrt{4+2.2.sqrt3+3}`

`=sqrt{(2+sqrt3)^2}`

`=|2+sqrt3|`

`=2+sqrt3`

\(\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\)

a/\(\sqrt{54}=3\sqrt{6}\)

b/\(\sqrt{50a}=\sqrt{50}.\sqrt{a}=5\sqrt{2}.\sqrt{a}\)

c/ \(\sqrt{5\left(\sqrt{3}\right)^2=}\sqrt{5.3}=\sqrt{15}\)

a) \(\sqrt{54}=\sqrt{9.6}=\sqrt{9}.\sqrt{6}=3\sqrt{6}\)

b) \(\sqrt{50a}=\sqrt{25.2a}=\sqrt{5^2.2a}=5\sqrt{2a}\)