Question

rút gọn

1, \(\sqrt{8-\sqrt{35}}\)

2, \(4\sqrt{3+2\sqrt{2}}-\sqrt{56\sqrt{2}+81}\)

3, \(\frac{x-49}{\sqrt{x}-7}\)

4, \(\sqrt{x+2\sqrt{x+1}}\)

5, \(\sqrt{x-1-2\sqrt{x-2}}\)

Answer 1

2.Ta có : \(4\sqrt{3+2\sqrt{2}}-\sqrt{56\sqrt{2}+81}\)

\(=4\sqrt{2+2\sqrt{2}+1}-\sqrt{56\sqrt{2}+81}\)

\(=4\sqrt{2}+4-\sqrt{56\sqrt{2}+81}\)

\(=4\sqrt{2}+4-\sqrt{7^2+2.4\sqrt{2}.7+\left(4\sqrt{2}\right)^2}\)

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

3.Ta có : \(\frac{x-49}{\sqrt{x}-7}\)

\(=\frac{\left(\sqrt{x}-7\right)\left(\sqrt{x}+7\right)}{\sqrt{x}-7}=\sqrt{x}+7\)

4.Ta có : \(\sqrt{x+2\sqrt{x+1}}\)

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

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

5.Ta có : \(\sqrt{x-1-2\sqrt{x-2}}\)

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

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