Question

Rationalize the denominatpr

1) 14÷5√3-√5
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Answer 1

Question :

$\mathsf{ \dfrac{14}{5 \sqrt{3} - \sqrt{5} } } \\ \\ \texttt{Rationalize the denominator.}$

$\mathfrak{Solution}$

$\mathsf{ \dfrac{14}{5 \sqrt{3} - \sqrt{5} }} \\ \\ \mathsf{ = \dfrac{14 (5 \sqrt{3} + \sqrt{5} )}{(5 \sqrt{3 } - \sqrt{5} )(5 \sqrt{3} + \sqrt{5} )}} \\ \\ \mathsf{ = \dfrac{14(5 \sqrt{3} + \sqrt{5} ) }{ ({5 \sqrt{3}) }^{2} - { (\sqrt{5} )}^{2} }} \\ \\ \mathsf{ = \dfrac{14(5 \sqrt{3} + \sqrt{5} ) }{75 - 5}} \\ \\ \mathsf{ = \dfrac{14(5 \sqrt{3} + \sqrt{5}) }{70}}\mathsf{ = \dfrac{5 \sqrt{3} + \sqrt{5} }{5}}.$

Answer 2

Answer:

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