\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
\(=\sqrt{\left(3\sqrt{5}\right)^2-2.3\sqrt{5}.1+1^2}-\sqrt{\left(2\sqrt{5}\right)^2-2.2\sqrt{5}.3+3^2}\)
\(=\sqrt{\left(3\sqrt{5}-1\right)^2}-\sqrt{\left(2\sqrt{5}-3\right)^2}=\left|3\sqrt{5}-1\right|-\left|2\sqrt{5}-3\right|\)
\(=3\sqrt{5}-1-2\sqrt{5}+3=\sqrt{5}+2\)
\(\sqrt{\left(3\sqrt{5}\right)^2-2\cdot3\sqrt{5}\cdot1+1^2}-\sqrt{\left(2\sqrt{5}\right)^2-2\cdot2\sqrt{5}\cdot3+3^2}\)
= \(\sqrt{\left(3\sqrt{5}-1\right)^2}-\sqrt{\left(2\sqrt{5}-3\right)^2}\)
= /\(3\sqrt{5}-1\)/ - /\(2\sqrt{5}-3\)/
= \(3\sqrt{5}-1-2\sqrt{5}+3\)
= \(\sqrt{5}+2\)
Lời giải:
** Bạn chú ý lần sau ghi đầy đủ yêu cầu đề.
\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}=\sqrt{45-2\sqrt{45}+1}-\sqrt{20-2\sqrt{20.9}+9}\)
\(=\sqrt{(\sqrt{45}-1)^2}-\sqrt{(\sqrt{20}-\sqrt{9})^2}=|\sqrt{45}-1|-|\sqrt{20}-\sqrt{9}|\)
\(=\sqrt{45}-1-(\sqrt{20}-\sqrt{9})=3\sqrt{5}-1-2\sqrt{5}+3=\sqrt{5}+2\)
\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
\(=3\sqrt{5}-1-2\sqrt{5}+3\)
\(=\sqrt{5}+2\)
