Ta có: \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)
\(=\sqrt{5-2\cdot\sqrt{5}\cdot\sqrt{3}+3}-\sqrt{3+2\cdot\sqrt{3}\cdot\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}\)
\(=\left|\sqrt{5}-\sqrt{3}\right|-\left|\sqrt{3}+\sqrt{5}\right|\)
\(=\sqrt{5}-\sqrt{3}-\sqrt{3}-\sqrt{5}\)
\(=-2\sqrt{3}\)
chứng minh \(\sqrt{8-2\sqrt{15}-\sqrt{8+2\sqrt{15}}}=-2\sqrt{3}\)
chứng minh
\(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}=-2\sqrt{3}\)
\(\sqrt{17+4\sqrt{15}}\) - \(\sqrt{8-2\sqrt{15}}\)
rút gọn B
B=\(\sqrt{8+2\sqrt{15}-2\sqrt{5}-2\sqrt{3}}\)-\(\sqrt{8-2\sqrt{15}-2\sqrt{5}+2\sqrt{3}}\)
\(\sqrt{\dfrac{8+\sqrt{15}}{2}+\dfrac{8-\sqrt{15}}{2}}\)
Rút gọn biểu thức:
A= \(\sqrt{\frac{8+\sqrt{15}}{2}}+\sqrt{\frac{8-\sqrt{15}}{2}}\)
Chứng minh
\(\left(\sqrt{4}-\sqrt{3}\right)^2=\sqrt{49}-\sqrt{48}\)
\(2\sqrt{2}\left(2-3\sqrt{3}\right)+\left(1-2\sqrt{2}\right)^2+6\sqrt{6}=9\)
\(\sqrt{8-2\sqrt{15}-\sqrt{8+2\sqrt{15}}}=-2\sqrt{3}\)
A=\(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{5}}\)
Chứng Minh Đẳng Thức :
\(\left(\sqrt{7+4\sqrt{3}}+\sqrt{8-2\sqrt{15}}\right)-\left(\sqrt{8+2\sqrt{15}}-\sqrt{7-4\sqrt{3}}\right)=0\)
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