Question

√(43+6√50)-√(43-6√50). Спростити

Answer 1

Ответ:

$\sqrt{43+6\sqrt{50}}-\sqrt{43-6\sqrt{50}}=\\\\=\sqrt{18+25+2\sqrt{18\cdot 25}}-\sqrt{18+25-2\sqrt{18\cdot 25}}=\\\\=\sqrt{(\sqrt{25}+\sqrt{18} )^2}-\sqrt{(\sqrt{25}-\sqrt{18} )^2}=|\sqrt{25}+\sqrt{18}|-|\sqrt{25}-\sqrt{18}|=\\\\=\sqrt{25}+\sqrt{18}-(\sqrt{25}-\sqrt{18})=2\sqrt{18}=6\sqrt2$