一道初中题——根式化简

hbghlyj

$7\sqrt{2(161-24\sqrt{2})}+\sqrt[4]2\sqrt{48+161\sqrt{2}}+14\sqrt{161-\sqrt{24769}}=8\sqrt{2(161+24\sqrt{2})}$

tommywong

對$\sqrt{161-\sqrt{24769}}$開方就證到架喇

個核心價值就係$\displaystyle\sqrt{a-\sqrt{b}}=\frac{\sqrt{a+\sqrt{a^2-b}}-\sqrt{a-\sqrt{a^2-b}}}{\sqrt{2}}$

$\displaystyle\sqrt{161-\sqrt{24769}}=\frac{\sqrt{161+24\sqrt{2}}-\sqrt{161-24\sqrt{2}}}{\sqrt{2}}$

力工

回复 2# tommywong
大佬！好墙！