Question

racionalize as frações

Answer 1

a)

$\frac{6}{1 + \sqrt{3}} * \frac{1 -\sqrt{3}}{1 -\sqrt{3}} = \frac{6(1 -\sqrt{3})}{1^{2} -\sqrt{3}^{2}}  = \frac{-2(-3 +3\sqrt{3})}{-2} = -3 +3\sqrt{3}$

b)

$\frac{11}{11-\sqrt{11} } * \frac{11+\sqrt{11} }{11+\sqrt{11} } = \frac{11(11+\sqrt{11} )}{11^{2} -\sqrt{11}^{2} } = \frac{11(11+\sqrt{11} )}{121 -11} = \frac{11(11+\sqrt{11} )}{11 * 10} = \frac{11 +\sqrt{11} }{10}$

c)

$\frac{1}{3 + \frac{\sqrt{13} }{2} } * \frac{3 - \frac{\sqrt{13} }{2} }{3 - \frac{\sqrt{13} }{2} } = \frac{3 - \frac{\sqrt{13} }{2} }{9 -\frac{13}{4} } = \frac{3 - \frac{\sqrt{13} }{2} }{\frac{(36 -13)}{4} } = \frac{4(3 - \frac{\sqrt{13} }{2} )}{23} = \frac{2(6 -\sqrt{13})}{23}$

d)

$\frac{1}{\sqrt{7}-3\sqrt{2}} * \frac{\sqrt{7}+3\sqrt{2}}{\sqrt{7}+3\sqrt{2}} = \frac{\sqrt{7}+3\sqrt{2}}{\sqrt{7}^{2}   - (3\sqrt{2})^{2} } = \frac{\sqrt{7}+3\sqrt{2}}{7 -9 * 2} = \frac{-\sqrt{7}-3\sqrt{2}}{11}$