Question

освободите от иррациональности в знаменателе дроби
$frac{6}{5 sqrt{3} }$
$frac{3}{ sqrt{11- sqrt{2} } }$

Answer 1

$frac{6}{5 sqrt{3} } = frac{6cdot sqrt{3}}{5 sqrt{3} cdot sqrt{3}}= frac{6sqrt{3}}{15} =frac{2sqrt{3}}{5}$

$frac{3}{ sqrt{11- sqrt{2} } }= frac{3sqrt{11- sqrt{2} }}{ (sqrt{11- sqrt{2} })^2 }= frac{3 sqrt{11- sqrt{2} }}{ 11- sqrt{2} }=$

$=frac{3 sqrt{11- sqrt{2} }cdot (11+ sqrt{2})}{ (11- sqrt{2})(11+ sqrt{2}) }=frac{3 sqrt{11- sqrt{2} }cdot (11+ sqrt{2})}{ 121-2 }=frac{3 sqrt{11- sqrt{2} }cdot (11+ sqrt{2})}{ (11- sqrt{2})(11+ sqrt{2}) }=$

$=frac{3 sqrt{11- sqrt{2} }cdot (11+ sqrt{2})}{ 119 }$