Question

thực hiện phép tính

\(\sqrt{2-\sqrt{3}}(\sqrt{5}+\sqrt{2})\)

Answer 1

\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)

= \(\sqrt{5}\sqrt{2-\sqrt{3}}+\sqrt{2}\sqrt{2-\sqrt{3}}\)

= \(\sqrt{5\left(2-\sqrt{3}\right)}+\sqrt{2\left(2-\sqrt{3}\right)}\)

= \(\sqrt{10-5\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)

= \(\sqrt{10-5\sqrt{3}}+\sqrt{3-2\sqrt{3}+1}\)

= \(\sqrt{10-5\sqrt{3}}+\sqrt{\left(\sqrt{3}-1\right)^2}\)

= \(\sqrt{10-5\sqrt{3}}+\sqrt{3}-1\)

\(\approx1,889524765....\)