Question

Вычислить рациональным способом
$( sqrt{ ( sqrt{2}- frac{3}{2} )^{2} } - sqrt[3]{(1- sqrt{2} )^{3} } )^{2}$

Answer 1

$sqrt{( sqrt{2}- frac{3}{2}) ^{2} }=| sqrt{2}- frac{3}{2}|=frac{3}{2}- sqrt{2} \ \ sqrt[3]{(1- sqrt{2}) ^{3} }=1- sqrt{2} \ \( sqrt{( sqrt{2}- frac{3}{2}) ^{2} }-sqrt[3]{(1- sqrt{2}) ^{3} }) ^{2}=(frac{3}{2}- sqrt{2} -(1- sqrt{2})) ^{2}= (frac{1}{2})^{2}= frac{1}{4}$