Question

racionalize os denominadres:
$\frac{3}{ \sqrt{7}+2 }$

$\frac{5}{2 \sqrt{3}-1 }$

Answer 1

a)
$\frac{3( \sqrt{7}-2) }{( \sqrt{7+2)( \sqrt{7}-2) } } = \frac{3( \sqrt{7}-2) }{ \sqrt{7^2}-2^2 } = \\ \\ \frac{3( \sqrt{7}-2) }{7-4} = \frac{3( \sqrt{7}-2) }{3} = \\ \\ 3( \sqrt{7}-2)=3 \sqrt{7} -6$

b)
$\frac{5(2 \sqrt{3}+1) }{(2 \sqrt{3}+1)(2 \sqrt{3}-1) } = \frac{5(2 \sqrt{3}+1) }{(2 \sqrt{3})^2-1^2 } = \\ \\ \frac{10 \sqrt{3}+5 }{12-1} = \frac{10 \sqrt{3}+5 }{11}$