Question

thực hiện phép tính \(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)

Answer 1

\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)=\dfrac{\sqrt{2}.\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\sqrt{4-2\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\sqrt{3-2\sqrt{3}+1}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\left|\sqrt{3}-1\right|\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\left(\sqrt{3}-1\right)\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\sqrt{15}+\sqrt{6}-\sqrt{5}-\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{30}+2\sqrt{3}-\sqrt{10}-2}{2}\)