giúp em vs ạ Bai2 Tíh,1) $\sqrt[3]{(4-2\sqrt3)(\sqrt3-1)}$ 2) $\sqrt[3]{(\sqrt2+1)(3+2\sqrt2)}$ $3)~\sqrt[3]{(\sqrt5+2)(9+4\sqrt5)}$,$4)~(\sqrt[3]2+1)(\sqrt[3]4-\sqrt[3]2+1)$ 5) $(\sqrt[3]9-\sqrt[3]6+\sqrt[3]4)(\sqrt[3]3+\sqrt[3]2)$

Question

giúp em vs ạ Bai2  Tíh,1) $\sqrt[3]{(4-2\sqrt3)(\sqrt3-1)}$ 2) $\sqrt[3]{(\sqrt2+1)(3+2\sqrt2)}$ $3)~\sqrt[3]{(\sqrt5+2)(9+4\sqrt5)}$,$4)~(\sqrt[3]2+1)(\sqrt[3]4-\sqrt[3]2+1)$ 5) $(\sqrt[3]9-\sqrt[3]6+\sqrt[3]4)(\sqrt[3]3+\sqrt[3]2)$

Accepted Answer

1) Ta có:
$$
\sqrt[3]{(4-2\sqrt{3})(\sqrt{3}-1)}
$$
Nhận thấy rằng:
$$
4 - 2\sqrt{3} = (\sqrt{3})^2 - 2\sqrt{3} + 1 = (\sqrt{3} - 1)^2
$$
Do đó:
$$
(4 - 2\sqrt{3})(\sqrt{3} - 1) = (\sqrt{3} - 1)^2 (\sqrt{3} - 1) = (\sqrt{3} - 1)^3
$$
Vậy:
$$
\sqrt[3]{(4 - 2\sqrt{3})(\sqrt{3} - 1)} = \sqrt[3]{(\sqrt{3} - 1)^3} = \sqrt{3} - 1
$$

2) Ta có:
$$
\sqrt[3]{(\sqrt{2} + 1)(3 + 2\sqrt{2})}
$$
Nhận thấy rằng:
$$
3 + 2\sqrt{2} = (\sqrt{2})^2 + 2\sqrt{2} + 1 = (\sqrt{2} + 1)^2
$$
Do đó:
$$
(\sqrt{2} + 1)(3 + 2\sqrt{2}) = (\sqrt{2} + 1)(\sqrt{2} + 1)^2 = (\sqrt{2} + 1)^3
$$
Vậy:
$$
\sqrt[3]{(\sqrt{2} + 1)(3 + 2\sqrt{2})} = \sqrt[3]{(\sqrt{2} + 1)^3} = \sqrt{2} + 1
$$

3) Ta có:
$$
\sqrt[3]{(\sqrt{5} + 2)(9 + 4\sqrt{5})}
$$
Nhận thấy rằng:
$$
9 + 4\sqrt{5} = (\sqrt{5})^2 + 4\sqrt{5} + 4 = (\sqrt{5} + 2)^2
$$
Do đó:
$$
(\sqrt{5} + 2)(9 + 4\sqrt{5}) = (\sqrt{5} + 2)(\sqrt{5} + 2)^2 = (\sqrt{5} + 2)^3
$$
Vậy:
$$
\sqrt[3]{(\sqrt{5} + 2)(9 + 4\sqrt{5})} = \sqrt[3]{(\sqrt{5} + 2)^3} = \sqrt{5} + 2
$$

4) Ta có:
$$
(\sqrt[3]{2} + 1)(\sqrt[3]{4} - \sqrt[3]{2} + 1)
$$
Nhận thấy rằng:
$$
\sqrt[3]{4} = (\sqrt[3]{2})^2
$$
Do đó:
$$
(\sqrt[3]{2} + 1)((\sqrt[3]{2})^2 - \sqrt[3]{2} + 1) = (\sqrt[3]{2})^3 + 1 = 2 + 1 = 3
$$

5) Ta có:
$$
(\sqrt[3]{9} - \sqrt[3]{6} + \sqrt[3]{4})(\sqrt[3]{3} + \sqrt[3]{2})
$$
Nhận thấy rằng:
$$
\sqrt[3]{9} = (\sqrt[3]{3})^2, \quad \sqrt[3]{6} = \sqrt[3]{3} \cdot \sqrt[3]{2}, \quad \sqrt[3]{4} = (\sqrt[3]{2})^2
$$
Do đó:
$$
((\sqrt[3]{3})^2 - \sqrt[3]{3} \cdot \sqrt[3]{2} + (\sqrt[3]{2})^2)(\sqrt[3]{3} + \sqrt[3]{2}) = (\sqrt[3]{3})^3 + (\sqrt[3]{2})^3 = 3 + 2 = 5
$$

Đáp số:
1) $\sqrt{3} - 1$
2) $\sqrt{2} + 1$
3) $\sqrt{5} + 2$
4) 3
5) 5