Question

[Yến Nhi]

Chứng minh đẳng thức:

\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)

\(\sqrt{23+8\sqrt{7}}-\sqrt{7=4}\)

Answer 1

[Hoàng Thanh Tuấn]

1. \(\sqrt{\sqrt{5}^2-2.2\sqrt{5}+4}-\sqrt{5}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}=\sqrt{5}-2-\sqrt{5}=-2\left(dpcm\right)\)
2. \(\sqrt{23+8\sqrt{7}}-\sqrt{7}=\sqrt{\sqrt{7}^2+2.4\sqrt{7}+16}-\sqrt{7}\)\(=\sqrt{\left(\sqrt{7}+4\right)^2}-\sqrt{7}=\sqrt{7}+4-\sqrt{7}=4\left(DPCM\right)\)