rút gọn biểu thức A=√(5+√21)+√(5-√21)-2√(4-√7)

     $A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}-2\sqrt{4-\sqrt{7}}$

⇔ $A\sqrt{2}=\sqrt{2}.(\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}-2\sqrt{4-\sqrt{7}})$

⇔ $A\sqrt{2}=\sqrt{2}.\sqrt{5+\sqrt{21}}+\sqrt{2}.\sqrt{5-\sqrt{21}}-2\sqrt{2}.\sqrt{4-\sqrt{7}}$

⇔ $A\sqrt{2}=\sqrt{2(5+\sqrt{21})}+\sqrt{2(5-\sqrt{21})}-2\sqrt{2(4-\sqrt{7})}$

⇔ $A\sqrt{2}=\sqrt{10+2\sqrt{21}}+\sqrt{10-2\sqrt{21}}-2\sqrt{8-2\sqrt{7}}$

⇔ $A\sqrt{2}=\sqrt{7+3+2\sqrt{7}.\sqrt{3}}+\sqrt{7+3-2\sqrt{7}.\sqrt{3}}-2\sqrt{7+1-2\sqrt{7}}$

⇔ $A\sqrt{2}$ $=$ $\sqrt{\sqrt{7}^2+\sqrt{3}^2+2\sqrt{7}.\sqrt{3}}$ $+$ $\sqrt{\sqrt{7}^2+\sqrt{3}^2-2\sqrt{7}.\sqrt{3}}$ $-$ $2\sqrt{\sqrt{7}^2+1^2-2\sqrt{7}.1}$

⇔ $A\sqrt{2}=\sqrt{(\sqrt{7}+\sqrt{3})^2}+\sqrt{(\sqrt{7}-\sqrt{3})^2}-2\sqrt{(\sqrt{7}-1)^2}$

⇔ $A\sqrt{2}=|\sqrt{7}+\sqrt{3}|+|\sqrt{7}-\sqrt{3}|-2|\sqrt{7}-1|$

⇔ $A\sqrt{2}=\sqrt{7}+\sqrt{3}+\sqrt{7}-\sqrt{3}-2\sqrt{7}+2$

⇔ $A\sqrt{2}=2$

⇔ $A=2:\sqrt{2}$

⇔ $A=\sqrt{2}$