Question

решите пожалуйста,срочно !

Answer 1

1)
$sqrt[3]{1- sqrt{2} } sqrt[6]{3+ 2sqrt{2} }=sqrt[6]{(1- sqrt{2})^2(3+ 2sqrt{2}) }= \ =sqrt[6]{(1- 2sqrt{2}+2)(3+ 2sqrt{2})}=sqrt[6]{(3- 2sqrt{2})(3+ 2sqrt{2})}= \ =sqrt[6]{9- 4*2}= sqrt[6]{1}=1$
2)
$(2,5^{ -frac{2}{9} })^{1,5}( frac{4}{25} )^{- frac{1}{6} }=(( frac{5}{2} )^{ -frac{2}{9} })^{ frac{3}{2} }( frac{2^2}{5^2} )^{- frac{1}{6} }=( frac{5}{2} )^{ -frac{1}{3} }( frac{2}{5} )^{- frac{1}{3} }=( frac{5}{2} * frac{2}{5} )^{- frac{1}{3} }=1$

3)
$sqrt{4+2 sqrt{3} }- sqrt{4-2 sqrt{3} } = (sqrt{4+2 sqrt{3} }- sqrt{4-2 sqrt{3} })* frac{sqrt{4+2 sqrt{3} }}{sqrt{4+2 sqrt{3} }}= \ = frac{4+2sqrt{3}- sqrt{16-4*3} }{sqrt{4+2 sqrt{3} }} = frac{4+2sqrt{3}- 2 }{sqrt{4+2 sqrt{3} }}=frac{2+2sqrt{3}}{sqrt{4+2 sqrt{3} }}=sqrt{ frac{(2+2 sqrt{3} )^2}{4+2 sqrt{3}} }= \ =sqrt{ frac{4+8 sqrt{3} +12}{4+2 sqrt{3}} }=sqrt{ frac{16+8 sqrt{3} }{4+2 sqrt{3}} }=2sqrt{ frac{4+2 sqrt{3} }{4+2 sqrt{3}} }=2$