Question

С 1 по 4 номер. Выбираю лучший ответ.

Answer 1

$1) sqrt[3]{ab}=sqrt[3]acdotsqrt[3]b,\a & bin mathbb R (B)$

$2) 3sqrt7=sqrt{3^2cdot7}=sqrt{63},\7sqrt{3}=sqrt{7^2cdot3}=sqrt{147},\sqrt{63} textless sqrt{147} Longrightarrow 3sqrt{7} textless 7sqrt{3};$

$3) left(sqrt8-3sqrt2+sqrt{10}right)left(sqrt2+sqrt{1,6}+3sqrt{0,4}right)=\=left(sqrt{2^3}-3sqrt2+sqrt{10right)left(sqrt2+sqrt{4cdot0,4}+3sqrt{0,4}right)=\=left(2sqrt{2}-3sqrt2+sqrt{10}right)left(sqrt2+2sqrt{0,4}+3sqrt{0,4}right)=\=left(-sqrt2+sqrt{10}right)left(sqrt2+5sqrt{0,4}right)=left(-sqrt2+sqrt{10}right)left(sqrt2+sqrt{5^2cdot0,4}right)=\=left(-sqrt2+sqrt{10}right)left(sqrt2+sqrt{10}right)=$
$=left(sqrt{10}-sqrt2right)left(sqrt{10}+sqrt2right)=left(sqrt{10}right)^2-left(sqrt2right)^2=10-2=8.$

$4) frac{sqrt x+1}{xsqrt x+x+sqrt x}:frac{1}{x^2-sqrt x}=frac{left(sqrt x+1right)left(x^2-sqrt xright)}{xsqrt x+x+sqrt x}=frac{x^2sqrt x-x+x^2-sqrt x}{xsqrt x+x+sqrt x}=\\=frac{left(x^2sqrt x -sqrt xright)+left(x^2-xright)}{xsqrt x+x+sqrt x}=frac{sqrt xleft(x^2 -1)+xleft(x-1right)}{xsqrt x+x+sqrt x}=\\=frac{sqrt xleft(x-1)(x+1)+xleft(x-1right)}{xsqrt x+x+sqrt x}=frac{(x-1)left(sqrt x(x+1)+xright)}{xsqrt x+x+sqrt x}=$

$=frac{(x-1)left(xsqrt x+sqrt x+xright)}{xsqrt x+x+sqrt x}=frac{(x-1)left(xsqrt x+x+sqrt xright)}{xsqrt x+x+sqrt x}=x-1.$