1/ Tính: \(\sqrt[3]{54}-\sqrt[3]{16}\)
2/ so sánh các cặp số sau
a) \(3\sqrt{2}\) và \(2\sqrt{3}\)
b) 4.\(\sqrt[3]{5}\) và 5.\(\sqrt[3]{4}\)
3/ cho biểu thức A= \(_{\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)}\)\(\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\)
a) tìm điều kiện x để A có nghĩa
b) Rút gọn A
2/
a) Ta có:
\(3\sqrt{2}=\sqrt{3^2\cdot2}=\sqrt{9\cdot2}=\sqrt{18}\)
\(2\sqrt{3}=\sqrt{2^2\cdot3}=\sqrt{4\cdot3}=\sqrt{12}\)
Mà: \(12< 18\Rightarrow\sqrt{12}< \sqrt{18}\Rightarrow2\sqrt{3}< 3\sqrt{2}\)
b) Ta có:
\(4\sqrt[3]{5}=\sqrt[3]{4^3\cdot5}=\sqrt[3]{320}\)
\(5\sqrt[3]{4}=\sqrt[3]{5^3\cdot4}=\sqrt[3]{500}\)
Mà: \(320< 500\Rightarrow\sqrt[3]{320}< \sqrt[3]{500}\Rightarrow4\sqrt[3]{5}< 5\sqrt[3]{4}\)
3/
a)ĐKXĐ: \(x\ne1;x\ge0\)
b) \(A=\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\)
\(A=\left[1-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right]\left[1+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\right]\)
\(A=\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)\)
\(A=1^2-\left(\sqrt{x}\right)^2\)
\(A=1-x\)
1/ \(\sqrt[3]{54}-\sqrt[3]{16}\)
\(=\sqrt[3]{3^3\cdot2}-\sqrt[3]{2^3\cdot2}\)
\(=3\sqrt[2]{3}-2\sqrt[3]{2}\)
\(=\left(3-2\right)\sqrt[3]{2}\)
\(=\sqrt[3]{2}\)