Question

Rút gọn các biểu thức :

a) \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)

b) \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

c)\(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

Answer 1

a: \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)

\(=4-\sqrt{15}+\sqrt{15}=4\)

b: \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

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

\(=2\sqrt{3}\)

c: \(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

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

\(=2\sqrt{5}+3-2\sqrt{5}+3=6\)