Question

Помогите пожалуйста срочно!!! С объяснением!!! Алгебра 8 класс!!!

Answer 1

$1); ; (3sqrt{6}+5sqrt{8}-4sqrt{32})cdot sqrt2-sqrt{108}=3sqrt{12}+5sqrt{16}-4sqrt{64}-sqrt{4cdot 27}=\\=3cdot 2sqrt3+5cdot 4-4cdot 8-2cdot 3sqrt3=20-32=-12\\\2); ; (sqrt5+7sqrt2)(7sqrt2-sqrt5)-(sqrt{10}-2sqrt5)^2=\\=(7sqrt2)^2-(sqrt5)^2-((sqrt{10})^2-2cdot sqrt{10}cdot 2sqrt5+(2sqrt5)^2)=\\=49cdot 2-5-10+4sqrt{50}-4cdot 5=63+4cdot 5sqrt2=63+20sqrt2$

$3); ; (7-sqrt3)^2+(4+sqrt3)^2=49-14sqrt3+3+16+8sqrt3+3=71-6sqrt3\\\4); ; (; sqrt{7-4sqrt3}+sqrt{7+4sqrt3}; )^2=7-4sqrt3+7+4sqrt3+2sqrt{(7-4sqrt3)(7+4sqrt3)}=\\=14+2sqrt{49-48}=14+2cdot 1=16$

$5); ; frac{x^2-11}{x+sqrt{11}}=frac{(x-sqrt{11})(x+sqrt{11})}{x+sqrt{11}}=x-sqrt{11}\\6); ; frac{sqrt{x}-12}{x-144}=frac{sqrt{x}-12}{(sqrt{x}-12)(sqrt{x}+12)}=frac{1}{sqrt{x}+12}\\7); ; frac{a+3sqrt{a}}{a-9}=frac{sqrt{a}, (sqrt{a}+3)}{(sqrt{a}-3)(sqrt{a}+3)}=frac{sqrt{a}}{sqrt{a}-3}\\8); ; frac{17-sqrt{17}}{sqrt{17}}=frac{sqrt{17}, (sqrt{17}-1)}{sqrt{17}}=sqrt{17}-1$

$9); ; frac{m-12sqrt{m}+36}{m-36}=frac{(sqrt{m}-6)^2}{(sqrt{m}-6)(sqrt{m}+6)}=frac{sqrt{m}-6}{sqrt{m}+6}\\10); ; frac{sqrt{21}-3}{7-sqrt{21}}=frac{sqrt3, (sqrt7-sqrt3)}{sqrt7, (sqrt7-sqrt3)}=frac{sqrt3}{sqrt7}=sqrt{frac{3}{7}}$