Question

Thực hiện phép tính:

a. \(\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}\)

b. \(\sqrt{33+8\sqrt{2}-\sqrt{33-8\sqrt{2}}}\)

Answer 1

\(\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}\)

\(=\sqrt{5}-\sqrt{3-\sqrt{\left(\sqrt{20}-3\right)^2}}\)

\(=\sqrt{5}-\sqrt{3-2\sqrt{5}+3}\)

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

\(=\sqrt{5}-\sqrt{5}+1=1\)

b)\(\sqrt{33+8\sqrt{2}-\sqrt{33-8\sqrt{2}}}\)

​​\(=\sqrt{33+8\sqrt{2}-\sqrt{\left(\sqrt{32}-1\right)^2}}\)

\(=\sqrt{33+8\sqrt{2}-\sqrt{32}+1}\)

\(=\sqrt{34+4\sqrt{2}}\)