Question

Racionalize
A)√7/2√3
B)3/√5+√3
D)7/√8-√2
E)3/2+√3
F)5/3+√2

Answer 1

$A) \frac{ \sqrt{7} }{2 \sqrt{3} } \to \frac{ \sqrt{7} }{2 \sqrt{3} } * \frac{2 \sqrt{3} }{2 \sqrt{3} } \to \frac{ 2\sqrt{21} }{4 \sqrt{9} } \to \frac{ 2\sqrt{21} }{4 *3 } \to \frac{ 2\sqrt{21} }{12 } \to \frac{ \sqrt{21} }{ 6 }$




$B) \frac{3}{ \sqrt{5} + \sqrt{3} } \to \frac{3}{ \sqrt{5} + \sqrt{3} } *\frac{\sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \to \frac{3(\sqrt{5} - \sqrt{3} )}{ \sqrt{25} - \sqrt{9} }\to \frac{3(\sqrt{5} - \sqrt{3} )}{ 5-3 }\to \frac{3(\sqrt{5} - \sqrt{3} )}{2 }$




$D) \frac{7}{ \sqrt{8} - \sqrt{2} } \to \frac{7}{ \sqrt{8} - \sqrt{2} }* \frac{\sqrt{8} + \sqrt{2} }{ \sqrt{8} + \sqrt{2} }\to \frac{7(\sqrt{8} + \sqrt{2}) }{ \sqrt{64} - \sqrt{4} }\to \frac{7(\sqrt{8} + \sqrt{2}) }{ 8-2 }\to \frac{7(\sqrt{8} + \sqrt{2}) }{ 6 }$




$E) \frac{3}{2+ \sqrt{3} } \to \frac{3}{2+ \sqrt{3} } *\frac{2- \sqrt{3} }{2- \sqrt{3} } \to \frac{3(2- \sqrt{3}) }{4-\sqrt{9} } \to \frac{6- 3\sqrt{3} }{4-3 } \to \frac{6- 3\sqrt{3} }{1 } \to 6- 3\sqrt{3}$




$F) \frac{5}{3+ \sqrt{2} } \to \frac{5}{3+ \sqrt{2} } *\frac{3- \sqrt{2} }{3- \sqrt{2} } \to \frac{5(3- \sqrt{2} )}{9- \sqrt{4} } \to \frac{15- 5\sqrt{2} }{9- 2} \to \frac{15- 5\sqrt{2} }{7}$