Question

Rút gọn :

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

Answer 1

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

\(=\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left[\left(\sqrt{2}-1\right)^2-\left(\sqrt{3}-1\right)+1\right]\)

\(=\left(\sqrt{2}-1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)-2\left(\sqrt{2}+1\right)\left(\sqrt{6}+1\right)+\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\)

\(=\left(\sqrt{6}+1\right)\left(\sqrt{6}-\sqrt{3}+\sqrt{2}-1-2\sqrt{2}-2+\sqrt{6}+\sqrt{3}+\sqrt{2}+1\right)\)

\(=\left(\sqrt{6}+1\right)\left(2\sqrt{6}-2\right)\)

\(=2\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)=10\)

Answer 2

@Khôi Bùi, @Ribi Nkok Ngok, @tran nguyen bao quan, @Nguyễn Thị Diễm Quỳnh, @Luân Đào

Giúp e vs!

Answer 3

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

\(=\left(\sqrt{6}+\sqrt{2}+\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

\(=\left(7+2\sqrt{6}+3\sqrt{3}+4\sqrt{2}\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

= 10