Tính \(\sqrt[3]{125}-\sqrt[3]{-8}+\sqrt{64}=?\) 11 15 12 10 Hướng dẫn giải: \(\sqrt[3]{125}-\sqrt[3]{-8}+\sqrt{64}=5-\left(-2\right)+8=15\).
Chọn câu SAI: \(\dfrac{\sqrt[3]{a}}{\sqrt[3]{b}}=\sqrt[3]{\dfrac{a}{b}}\left(b\ne0\right)\) \(a^3=b^3\Leftrightarrow a=b\) \(a< b\Leftrightarrow\sqrt[3]{a}< \sqrt[3]{b}\) \(\sqrt[3]{a^3.b}=\left|a\right|.\sqrt[3]{b}\)
Rút gọn biểu thức : \(\sqrt[3]{\left(a+b\right)^3}+\sqrt[3]{\left(a-b\right)^3}\) \(2a\) \(a+b\) \(\left|a+b\right|+\left|a-b\right|\) \(2b\) Hướng dẫn giải: \(\sqrt[3]{\left(a+b\right)^3}+\sqrt[3]{\left(a-b\right)^3}\) \(=a+b+a-b=2a\)
Tính: \(\sqrt[3]{20-14\sqrt{2}}.\sqrt[3]{20+14\sqrt{2}}\) \(2\) \(8\) \(4\) \(6\) Hướng dẫn giải: \(\sqrt[3]{20-14\sqrt{2}}.\sqrt[3]{20+14\sqrt{2}}=\sqrt[3]{\left(20-14\sqrt{2}\right)\left(20+14\sqrt{2}\right)}=\)\(\sqrt[3]{20^2-\left(14\sqrt{2}\right)^2}=\sqrt[3]{8}=2\).
Trục căn thức ở mẫu biểu thức \(\dfrac{1}{\sqrt[3]{4}+\sqrt[3]{5}}\) \(\dfrac{\sqrt[3]{4^2}-\sqrt[3]{4}.\sqrt[3]{5}+\sqrt[3]{5^2}}{9}\) \(=\dfrac{\sqrt[3]{4^2}+\sqrt[3]{4}.\sqrt[3]{5}+\sqrt[3]{5^2}}{9}\) \(\dfrac{\sqrt[3]{4}-\sqrt[3]{5}}{9}\) \(\sqrt[3]{4}-\sqrt[3]{5}\) Hướng dẫn giải: \(\dfrac{1}{\sqrt[3]{4}+\sqrt[3]{5}}\) \(=\dfrac{1.\left(\sqrt[3]{4^2}-\sqrt[3]{4}.\sqrt[3]{5}+\sqrt[3]{5^2}\right)}{\left(\sqrt[3]{4}+\sqrt[3]{5}\right)\left(\sqrt[3]{4^2}-\sqrt[3]{4}.\sqrt[3]{5}+\sqrt[3]{5^2}\right)}\) \(=\dfrac{\sqrt[3]{4^2}-\sqrt[3]{4}.\sqrt[3]{5}+\sqrt[3]{5^2}}{4+5}\) \(=\dfrac{\sqrt[3]{4^2}-\sqrt[3]{4}.\sqrt[3]{5}+\sqrt[3]{5^2}}{9}\)
Tính \(\left(\sqrt[3]{16}-\sqrt[3]{12}+\sqrt[3]{9}\right)\left(\sqrt[3]{4}+\sqrt[3]{3}\right)\) \(7\) \(6\) \(5\) \(4\) Hướng dẫn giải: \(\left(\sqrt[3]{16}-\sqrt[3]{12}+\sqrt[3]{9}\right)\left(\sqrt[3]{4}+\sqrt[3]{3}\right)\) \(=\left(\sqrt[3]{4}\right)^3+\left(\sqrt[3]{3}\right)^3=4+3=7\)
Rút gọn biểu thức \(\left(\dfrac{2x+1}{\sqrt{x^3}-1}-\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\right).\left(\dfrac{1+\sqrt{x^3}}{1+\sqrt{x}}-\sqrt{x}\right)\) \(\sqrt{x}-1\) \(2\sqrt{x}-1\) \(x-\sqrt{x}+1\) \(3\sqrt{x}+1\) Hướng dẫn giải: \(\left(\dfrac{2x+1}{\sqrt{x^3}-1}-\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\right).\left(\dfrac{1+\sqrt{x^3}}{1+\sqrt{x}}-\sqrt{x}\right)\) \(=\dfrac{2x+1-\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\left[\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{1+\sqrt{x}}-\sqrt{x}\right]\) \(=\dfrac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\left(1-2\sqrt{x}+x\right)\) \(=\dfrac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\left(\sqrt{x}-1\right)^2\) \(=\sqrt{x}-1\)
Tính \(\sqrt{3\dfrac{1}{2}}.\sqrt{3\dfrac{3}{7}}.\sqrt{12}\) \(12\) \(14\) \(15\) \(16\) Hướng dẫn giải: \(\sqrt{3\dfrac{1}{2}}.\sqrt{3\dfrac{3}{7}}.\sqrt{12}\) \(=\sqrt{\dfrac{7}{2}}.\sqrt{\dfrac{24}{7}}.\sqrt{12}\) \(=\sqrt{\dfrac{7}{2}.\dfrac{24}{7}.12}=12\)
Rút gọn biểu thức \(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}+\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\) \(2+\sqrt{3}\) \(2-\sqrt{3}\) \(\sqrt{3}\) \(2\sqrt{3}\) Hướng dẫn giải: \(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}+\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\) \(=\dfrac{2\left(\sqrt{3}+1\right)-2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}+\dfrac{\sqrt{3}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}\) \(=\dfrac{2\sqrt{3}+2-2\sqrt{3}+2}{2}+\sqrt{3}\) \(=2+\sqrt{3}\)
