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Đặt \(2000=a\)
\(A=a^9\\ B=\left(a-4\right)\left(a-3\right)\left(a-2\right)\left(a-1\right)a\left(a+1\right)\left(a+2\right)\left(a+3\right)\left(a+4\right)\\ B=\left(a^2-16\right)\left(a^2-9\right)\left(a^2-4\right)\left(a^2-1\right)a< a.a^2.a^2.a^2.a^2=a^9\\ B=\left(a-8\right)\left(a-6\right)\left(a-4\right)\left(a-2\right)a\left(a+2\right)\left(a+4\right)\left(a+6\right)\left(a+8\right)\\ C=\left(a^2-64\right)\left(a^2-36\right)\left(a^2-16\right)\left(a^2-4\right)a\\ C< \left(a^2-9\right)\left(a^2-4\right)\left(a^2-1\right)a< a.a^2.a^2.a^2=a^9\\ D=\left(a-20\right)\left(a-15\right)\left(a-10\right)\left(a-5\right)a\left(a+5\right)\left(a+10\right)\left(a+15\right)\left(a+20\right)\\ D=\left(a^2-400\right)\left(a^2-225\right)\left(a^2-100\right)\left(a^2-25\right)a\\ D< \left(a^2-64\right)\left(a^2-36\right)\left(a^2-16\right)\left(a^2-4\right)a< a.a^2.a^2.a^2=9\)
Vậy \(D< C< B< A\)
`\sqrt{2}.\sqrt{18}=\sqrt{2.18}=\sqrt{36}=6`
`\sqrt{5}.\sqrt{20}=\sqrt{5.20}=\sqrt{100}=10`
\(3\sqrt{25}-\sqrt{36}-2\sqrt{16}=\sqrt{225}-\sqrt{36}-\sqrt{64}=15-6-8=1\)
A = sin 2 15 0 + sin 2 25 0 + sin 2 35 0 + sin 2 45 0 + sin 2 55 0 + sin 2 65 0 + sin 2 75 0
Ta có:
A = sin 2 15 0 + sin 2 25 0 + sin 2 35 0 + sin 2 45 0 + sin 2 55 0 + sin 2 65 0 + sin 2 75 0
= sin 2 15 0 + sin 2 25 0 + sin 2 35 0 + sin 2 45 0 + cos 2 35 0 + cos 2 25 0 + cos 2 15 0
= ( sin 2 15 0 + cos 2 15 0 ) + ( sin 2 25 0 + cos 2 25 0 ) + ( sin 2 35 0 + cos 2 35 0 ) + sin 2 45 0
= 1 + 1 + 1 + 2 2 2 = 3 + 1 2 = 7 2
Đáp án cần chọn là: B
\(\sqrt{\dfrac{49}{100}}=\dfrac{7}{10}\\ \sqrt{\dfrac{144}{289}}=\dfrac{12}{17}\\ \dfrac{\sqrt{36}}{\sqrt{225}}=\dfrac{6}{15}=\dfrac{2}{5}\\ \dfrac{\sqrt{25}}{\sqrt{121}}=\dfrac{5}{11}\)
`\sqrt{(3-\sqrt{5})^2}+\sqrt{5}=|3-\sqrt{5}|+\sqrt{5}=3-\sqrt{5}+\sqrt{5}=3`
`\sqrt{3}-\sqrt{(1+\sqrt{3})^2}=\sqrt{3}-|1+\sqrt{3}|=\sqrt{3}-1-\sqrt{3}=-1`
`\sqrt{(\sqrt{3}-1)^2}-\sqrt{3}=|\sqrt{3}-1|-\sqrt{3}=\sqrt{3}-1-\sqrt{3}=-1`
\(\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{5}=\left|3-\sqrt{5}\right|+\sqrt{5}=3-\sqrt{5}+\sqrt{5}=3\)
\(\sqrt{3}-\sqrt{\left(1+\sqrt{3}\right)^2}=\sqrt{3}-\left|1+\sqrt{3}\right|=\sqrt{3}-1-\sqrt{3}=-1\)
\(\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}=\left|\sqrt{3}-1\right|-\sqrt{3}=\sqrt{3}-1-\sqrt{3}=-1\)
20
7
\(\sqrt{16.25}=\sqrt{400}=20\)
\(\sqrt{0,25.196}=\sqrt{49}=7\)