Question

\(\sqrt{3-2\sqrt{ }2}+\sqrt{4-2\sqrt{ }3}-\sqrt{7-4\sqrt{ }3}\)

Mấy bn giúp mk vs ạ....

Answer 1

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

Tương tự  \(\sqrt{4-2\sqrt{3}}=\sqrt{3}-1\);   \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)

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

Answer 2

\(\sqrt{3-2\sqrt{2}}+\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

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

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

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

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

Answer 3

ok nhé