Question

Rút Gọn \(\sqrt{8+3\sqrt{7}}-\sqrt{8-3\sqrt{7}}\)

Answer 1

\(\sqrt{8+3\sqrt{7}}-\sqrt{8-3\sqrt{7}}\)

\(=\frac{\sqrt{16+6\sqrt{7}}}{\sqrt{2}}-\frac{\sqrt{16-6\sqrt{7}}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{7}\right)^2+2.\sqrt{7}.3+3^2}}{\sqrt{2}}-\frac{\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}.3+3^2}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{7}+3\right)^2}}{\sqrt{2}}-\frac{\sqrt{\left(3-\sqrt{7}\right)^2}}{\sqrt{2}}\)

\(=\frac{\sqrt{7}+3}{\sqrt{2}}-\frac{3-\sqrt{7}}{\sqrt{2}}\)

\(=\frac{\sqrt{7}+3-3+\sqrt{7}}{\sqrt{2}}=\frac{2\sqrt{7}}{\sqrt{2}}=\sqrt{14}\)

Answer 2

Thanks bn♥