Question

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

Answer 1

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

\(=\sqrt{\left(\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}\right)^2}-\sqrt{\left(\sqrt{\frac{7}{2}}+\sqrt{\frac{1}{2}}\right)^2}\)

\(=\left|\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}\right|-\left|\sqrt{\frac{7}{2}}+\sqrt{\frac{1}{2}}\right|\)

\(=\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}-\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}\)

\(=-\sqrt{\frac{1}{2}}-\sqrt{\frac{1}{2}}\)

\(=-\sqrt{2}\)

(Chúc bạn học tốt và k cho mình với nha!)