Đáp án:
\(1/\\ C_1=\left (-\sqrt{5} \right )+15\sqrt{2}\\ 2/\\ a,\ A=2\sqrt{3}\\ b,\ B=5.\left (\sqrt{2}+2-\sqrt{10} \right )\\ c,\ C=1\\ d,\ D=2\sqrt{6}\)
Giải thích các bước giải:
\(1/\\ \ c,\ C_1=\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\\ ⇔C_1=2\sqrt{5}-3\sqrt{5}+9\sqrt{2}+6\sqrt{2}\\ ⇔C_1=\left (2\sqrt{5}-3\sqrt{5} \right )+\left (9\sqrt{2}+6\sqrt{2} \right )\\ ⇔C_1=\left (-\sqrt{5} \right )+15\sqrt{2}\\ 2/\\ a,\ A=2\sqrt{3}+\sqrt{5}.\sqrt{3}-\sqrt{60}+\sqrt{15}\\ ⇔A=2\sqrt{3}+\sqrt{15}-2\sqrt{15}+\sqrt{15}\\ ⇔A=2\sqrt{3}+\left (\sqrt{15}-2\sqrt{15}+\sqrt{15} \right )\\ ⇔A=2\sqrt{3}\\ b,\ B=5\sqrt{2}+2\sqrt{5}.\sqrt{5}-\sqrt{250}\\ ⇔B=5\sqrt{2}+2\sqrt{25}-5\sqrt{10}\\ ⇔B=5\sqrt{2}+2.5-5\sqrt{10}\\ ⇔B=5.\left (\sqrt{2}+2-\sqrt{10} \right )\\ c,\ C=\sqrt{1+\sqrt{2}}.\sqrt{2+\sqrt{3}}.\sqrt{\sqrt{2}-1}.\sqrt{2-\sqrt{3}}\\ ⇔C=\left [\left (\sqrt{1+\sqrt{2}} \right ).\left (\sqrt{\sqrt{2}-1} \right )\right ].\left [\left (\sqrt{2+\sqrt{3}} \right ).\left (\sqrt{2-\sqrt{3}} \right ) \right ]\\ =\left (\sqrt{2-1} \right ).\left (\sqrt{4-3} \right )\\ =1.1\\ =1\\ d,\ D=\left (\sqrt{2}+\sqrt{3}+\sqrt{5} \right ).\left (\sqrt{2}+\sqrt{3}-\sqrt{5} \right )\\ ⇔D=\left (\sqrt{2}+\sqrt{3} \right )^{2}-\left (\sqrt{5} \right )^{2}\\ ⇔D=2+2\sqrt{6}+3-5\\ ⇔D=\left (2+3-5 \right )+2\sqrt{6}\\ ⇔D=2\sqrt{6}\)
chúc bạn học tốt!
