Question

[Uyên Dii]

Rút gọn

1. \(\left(\sqrt{12}+2\sqrt{27}-\sqrt{3}\right):\sqrt{3}\)
2. \(\left(4\sqrt{2}-\sqrt{8}+2\right).\sqrt{2-\sqrt{8}}\)
3. \(\sqrt{3}\left(2\sqrt{27}-\sqrt{75}+\frac{3}{2}\sqrt{12}\right)\)

Answer 1

[công chúa xinh xắn]

\(\left(\sqrt{12}+2\sqrt{27}-\sqrt{3}\right):\sqrt{3}\)

\(=\sqrt{12}:\sqrt{3}+2\sqrt{27}:\sqrt{3}-\sqrt{3}:\sqrt{3}\)

\(=\sqrt{4}+2\sqrt{9}-1\)

\(=2+6-1\)

\(=7\)

Answer 2

[Despacito]

2) \(\left(4\sqrt{2}-\sqrt{8}+2\right).\sqrt{2-\sqrt{8}}\)

\(=\left(4\sqrt{2}-2\sqrt{2}+2\right).\sqrt{2-2\sqrt{2}}\)

\(=\left(2\sqrt{2}+2\right)^2.\left(\sqrt{2-2\sqrt{2}}\right)^2\)

\(=\left(8+4\right)\left(2-2\sqrt{2}\right)\)

\(=12.\left(2-2\sqrt{2}\right)\)

\(=24-24\sqrt{2}\)

\(=24\left(1-\sqrt{2}\right)\)

3) \(\sqrt{3}\left(2\sqrt{27}-\sqrt{75}+\frac{3}{2}\sqrt{12}\right)\)

\(=\sqrt{3}\left(2\sqrt{3^2.3}-\sqrt{5^2.3}+\frac{3}{2}\sqrt{2^2.3}\right)\)

\(=\sqrt{3}\left(6\sqrt{3}-5\sqrt{3}+3\sqrt{3}\right)\)

\(=\sqrt{3}.4\sqrt{3}\)

\(=12\)