Question

Rationalise the denominater :
1) 5 / √3 - √5
2) 1 / √7 + √11​

Answer 1

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Answer 2

Answer:

(i)

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

(ii)

$= \frac{- \sqrt{7} + \sqrt{11} }{4}$

Step-by-step explanation:

(i)

$\frac{5}{ \sqrt{3} - \sqrt{5} } = \frac{5( \sqrt{3} + \sqrt{5} ) }{( \sqrt{3} - \sqrt{5})( \sqrt{3} + \sqrt{5}) }$

$\frac{5 \sqrt{3} + 5 \sqrt{5} }{( \sqrt{3} )^{2} - ( \sqrt{5})^{2} } = \frac{5 \sqrt{3} + 5 \sqrt{5} }{3 - 5}$

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

(ii)

$\frac{1}{ \sqrt{7} + \sqrt{11} } = \frac{1( \sqrt{7} - \sqrt{11}) }{( \sqrt{7} - \sqrt{11})( \sqrt{7} + \sqrt{11} ) }$

$\frac{ \sqrt{7} - \sqrt{11} }{( \sqrt{7}) ^{2} - ( \sqrt{11})^{2} } = \frac{ \sqrt{7} - \sqrt{11} }{7 - 11}$

$= \frac{- \sqrt{7} + \sqrt{11} }{4}$