Question

Rút gọn biểu thức

a)A=\(\sqrt{3-2\sqrt{2}}\)

b)B=\(\sqrt{3-2\sqrt{2}}-\sqrt{6+4\sqrt{2}}\)

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

Answer 1

a) \(A=\sqrt{3-2\sqrt{2}}=\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{2}-1\)

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

c) \(C=\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}=\dfrac{\sqrt{2}\left(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\right)}{\sqrt{2}}=\dfrac{\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{3}+1+\sqrt{3}-1}{\sqrt{2}}=\dfrac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\)