Question

ПОМОГИТЕ ПОЖАЛУЙСТА!!!
1) $frac{100}{ sqrt{11-6 sqrt{2 } +1} }$
2)$frac{ sqrt{2- sqrt{3} } }{ sqrt{2+ sqrt{3} } }$
3)(3+2√2)*(1-√2)²
4)$sqrt{23-4 sqrt{15} }$
5) (√a³b-√ab)²
6)$( 2+ frac{ sqrt{x} }{ sqrt{x} +1} ) * frac{3x + 3 sqrt{x} }{1 2sqrt{x} + 8}$
7)x2 -3√2 +2 ghb x=√2 +1

Answer 1

$1) 100/(sqrt{11-6 sqrt{2} } +1)=100/( sqrt{(3- sqrt{2} )^2} +1)=$$100/(3- sqrt{2} +1)=100/(4- sqrt{2} )=100(4+ sqrt{2} )/(4- sqrt{2} )(4+ sqrt{2} )=$$100(4+ sqrt{2} )/(16-2)=100(4+ sqrt{2} )/14=50(4+ sqrt{2} )/7$
$2) sqrt{2- sqrt{3} } / sqrt{2+ sqrt{3} } = sqrt{(2- sqrt{3} )^2} / sqrt{(2- sqrt{3})(2+ sqrt{3} ) }=$$(2- sqrt{3} )/ sqrt{4-3} =2- sqrt{3}$
$3)(3+2 sqrt{2} )(1- sqrt{2} )^2=(1+ sqrt{2} )^2*(1- sqrt{2} )^2=$$[(1- sqrt{2} )(1+ sqrt{2} )]^2=(1-2)^2=(-1)^2=1$
$4) sqrt{23-4 sqrt{15} } = sqrt{(2 sqrt{5}- sqrt{3} )^2 } =2 sqrt{5} - sqrt{3}$
$5)( sqrt{a^3b} - sqrt{ab} )^2=[ sqrt{ab} *(a-1)]^2=ab(a-1)^2$
6
1)2+ √x/(√x +1)=(2√x+2+√x)/(√x +1)=(2+3√x)/(√x +1)
2)(2+3√x)/(√x+1) *3√x(√x+1)/4(3√x+2)=3√x/4