Question

[nguyen dieu hoa]

Rút gọn :

a) \((2+\sqrt{3})\sqrt{7-4\sqrt{3}}\)

b) \(\sqrt{(1-\sqrt{2023})^2}\cdot\sqrt{2024+2\sqrt{2023}}\)

Answer 1

[Phước Lộc]

a) \((2+\sqrt{3})\sqrt{7-4\sqrt{3}}\)

\(=(2+\sqrt{3})\sqrt{4-4\sqrt{3}+3}\)

\(=(2+\sqrt{3})\sqrt{(2-\sqrt{3})^2}\)

\(=(2+\sqrt{3})(2-\sqrt{3})=4-3=1\)

b) \(\sqrt{(1-\sqrt{2023})^2}\cdot\sqrt{2024+2\sqrt{2023}}\)

\(=|1-\sqrt{2023}|\sqrt{2023+2\sqrt{2023}+1}\)

\(=(\sqrt{2023}-1)\sqrt{(\sqrt{2023}+1)^2}\)

\(=(\sqrt{2023}-1)(\sqrt{2023}+1)\)

\(=\sqrt{2023^2}-1^2=2023-1=2022\)