Giúp nhanh với ạ
a,\(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
\(=\sqrt{\dfrac{2\left(2+\sqrt{3}\right)}{2}}-\sqrt{\dfrac{2\left(2-\sqrt{3}\right)}{2}}\)
\(=\dfrac{\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\left|\sqrt{3}+1\right|-\left|\sqrt{3}-1\right|}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}+1-\left(\sqrt{3}-1\right)}{\sqrt{2}}\)
\(=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)
d/\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{\dfrac{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}{4+\sqrt{15}}}\)
\(=\sqrt{4+\sqrt{15}}\cdot\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\sqrt{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}\)
\(=\sqrt{8+2\sqrt{15}}\cdot\left(\sqrt{5}-\sqrt{3}\right)\sqrt{1}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\cdot\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\left|\sqrt{5}+\sqrt{3}\right|\cdot\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\left(\sqrt{5}+\sqrt{3}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)
\(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
\(=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{\left(4-\sqrt{2}\right)^2}}}\)
\(=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\left|4-\sqrt{2}\right|}}\)
\(=\sqrt{6-2\sqrt{2\sqrt{3}+4}}\)
\(=\sqrt{6-2\sqrt{\left(\sqrt{3}+1\right)^2}}\)
\(=\sqrt{6-2\left|\sqrt{3}+1\right|}\)
\(=\sqrt{6-2\text{}\left(\sqrt{3}+1\right)}\)
\(=\sqrt{4-2\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)
