\(9\sqrt{\dfrac{9}{4}-\sqrt{2}}=9\sqrt{\dfrac{9-4\sqrt{2}}{4}}=9\sqrt{\dfrac{\left(2\sqrt{2}-1\right)^2}{2^2}}=9.\left(\dfrac{2\sqrt{2}-1}{2}\right)=\dfrac{18\sqrt{2}-9}{2}\)
\(\sqrt{\dfrac{129}{16}+\sqrt{2}}=\sqrt{\dfrac{129+16\sqrt{2}}{16}}=\sqrt{\dfrac{\left(8\sqrt{2}+1\right)^2}{4^2}}=\dfrac{8\sqrt{2}+1}{4}\)
\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}=\sqrt{\dfrac{\left(12\sqrt{2}+1\right)^2}{4^2}}=\dfrac{12\sqrt{2}+1}{4}\)
\(\sqrt{2}.\sqrt{7.3\sqrt{5}}\)? Em kiểm tra lại đề câu d, \(\sqrt{7-3\sqrt{5}}\) hoặc \(\sqrt{7+3\sqrt{5}}\) mới đúng
\(\sqrt{2}.\sqrt{4+\sqrt{15}}=\sqrt{8+2\sqrt{15}}=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}+\sqrt{3}\)
\(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}=\sqrt{\dfrac{59+30\sqrt{2}}{25}}=\sqrt{\dfrac{\left(5\sqrt{2}+3\right)^2}{5^2}}=\dfrac{5\sqrt{2}+3}{5}\)
