Question

Rationalise the denominator 1/√6+√5-√11

Answer 1

Step-by-step explanation:

$\green{question::}$

$rationalize \: \frac{1}{ \sqrt{6} + \sqrt{5} - \sqrt{11} }$

${here\:we\:go\:with\:the\:solution}$

$to \: rationalize \: we \: multiply \: \\ the \: denominator \: at \: both \: sides$

$\frac{1}{ \sqrt{6} + \sqrt{5} - \sqrt{11} } \times \frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{ \sqrt{6} + \sqrt{5} - \sqrt{11} }$

$\frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{( { \sqrt{6 }+ \sqrt{5) } }^{2} - ( {11)}^{2} }$

$\frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{(6 + 5 + 2 \sqrt{30} - 11)}$

$\frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{2 \sqrt{30} }$

$again \: rationallizing$

$\frac{ \sqrt{6} + \sqrt{5} + \sqrt{11} }{2 \sqrt{30} } \times \frac{ \sqrt{30} }{ \sqrt{30} }$

$\frac{ \sqrt{180} + \sqrt{150} + \sqrt{330} }{60}$

$\frac{6 \sqrt{5} + 5 \sqrt{6} + \sqrt{330} }{60}$

$is \: your \: answer \\ thank \: you$