Question

solve this question .....

Answer 1

The answers are given below :

1.

Now,

$\frac{2 - \sqrt{3} }{ \sqrt{11} - \sqrt{7} } \\ \\ We \: \: rationalise \: \: the \: \: denomintor \\ by \: \: multiplying \: \: both \: \: the \\ numerator \: \: and \: \: denominator \\ by \: \: ( \sqrt{11} + \sqrt{7} ). \\ \\ So, \: \: \frac{(2 - \sqrt{3} )( \sqrt{11} + \sqrt{7} )}{( \sqrt{11} - \sqrt{7} )( \sqrt{11} + \sqrt{7}) } \\ \\ = \frac{2 \sqrt{11} + 2 \sqrt{7} - \sqrt{3} \sqrt{11} - \sqrt{3} \sqrt{7} }{11 - 7} \\ \\ = \frac{2 \sqrt{11} + 2 \sqrt{7} - \sqrt{33} - \sqrt{21} }{4} \\ \\ Hence, \: \: the \: \: denominator \: \: is \\ rationalised.$

2.

Now,

$\frac{3 - \sqrt{11} }{5 - 3 \sqrt{7} } \\ \\ We \: \: multiply \: \: both \: \: the \\ numerator \: \: and \: \: the \: \: \\ denominator \: \: by \: \: (5 + 3 \sqrt{7} ) \\ to \: \: rationalise \: \: the \\ denominator. \\ \\ So, \: \: \frac{(3 - \sqrt{11} )(5 + 3 \sqrt{7} )}{(5 - 3 \sqrt{7} )(5 + 3 \sqrt{7} )} \\ \\ = \frac{15 + 9 \sqrt{7} - 5 \sqrt{11} - 3 \sqrt{7} \sqrt{11} }{25 - 63} \\ \\ = \frac{15 + 9 \sqrt{7} - 5 \sqrt{11} - 3 \sqrt{21} }{ - 38} \\ \\ Hence, \: \: the \: \: denominator \: \: is \\ rationalised.$

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