Question

Rút gọn: 

A) \(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)

B) \(\sqrt{9-4\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)

 

Answer 1

A)\(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}=\sqrt{5-2\sqrt{5}.2+4}+\sqrt{5+2\sqrt{5}.1+1}\)

=\(\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}=\sqrt{5}-2+\sqrt{5}+1=2\sqrt{5}-1\)

b)\(\sqrt{9-4\sqrt{2}}-\sqrt{11+6\sqrt{2}}=\sqrt{9-2.\sqrt{4}\sqrt{2}}-\sqrt{9+2.3\sqrt{2}+2}\)

=\(\sqrt{8-2\sqrt{8}+1}-\sqrt{9+2.3\sqrt{2}+2}=\sqrt{\left(\sqrt{8}-1\right)^2}-\sqrt{\left(3+\sqrt{2}\right)^2}\)

=\(\sqrt{8}-1-3-\sqrt{2}=\sqrt{8}-\sqrt{2}-4\)