Question

Упростите выражение: √((9√18-√3)/(√18-√3)+√6) -√((6√3-10)^2 )

Answer 1

$sqrt{left[(9sqrt{18}-sqrt3):(sqrt{18}-sqrt3)right]+sqrt6}-sqrt{left(6sqrt3-10right)^2}\\=sqrt{left[(9sqrt{9cdot2}-sqrt3):(sqrt{9cdot2}-sqrt3)}right]+sqrt6}-|6sqrt3-10|\\=sqrt{left[(27sqrt2-sqrt3):(3sqrt2-sqrt3)right]+sqrt6}-(6sqrt3-10)\\=sqrt{frac{27sqrt2-sqrt3}{3sqrt2-sqrt3}cdotfrac{3sqrt2+sqrt3}{3sqrt2+sqrt3}+sqrt6}-6sqrt3+10$

$=sqrt{frac{81cdot2+27sqrt6-3sqrt6-3}{(3sqrt2)^2-(sqrt3)^2}+sqrt6}-6sqrt3+10\\=sqrt{frac{159+24sqrt6}{9cdot2-3}+sqrt6}-6sqrt3+10\\=sqrt{frac{159+24sqrt6}{18-3}+sqrt6}-6sqrt3+10\\=sqrt{frac{159+24sqrt6}{15}+sqrt6}-6sqrt3+10\\=sqrt{frac{53+8sqrt6}{5}+sqrt6}-6sqrt3+10\\=sqrt{frac{53+8sqrt6}{5}+frac{5sqrt6}{5}}-6sqrt3+10\\=sqrt{frac{53+13sqrt6}{5}}-6sqrt3+10$