Question

rationalise the denominator 5/root 13 - 2 root 2​

Answer 1

SOLUTION

TO DETERMINE

Rationalize the denominator

$\displaystyle \sf{ \frac{5}{ \sqrt{13} - 2 \sqrt{2} } }$

EVALUATION

$\displaystyle \sf{ \frac{5}{ \sqrt{13} - 2 \sqrt{2} } }$

$\displaystyle \sf{ = \frac{5(\sqrt{13} + 2 \sqrt{2}) }{ (\sqrt{13} - 2 \sqrt{2} )(\sqrt{13} + 2 \sqrt{2} )} }$

$\displaystyle \sf{ = \frac{5(\sqrt{13} + 2 \sqrt{2}) }{ {( \sqrt{13} )}^{2} - {(2 \sqrt{2}) }^{2} } }$

$\displaystyle \sf{ = \frac{5(\sqrt{13} + 2 \sqrt{2}) }{ (13 - 8)} }$

$\displaystyle \sf{ = \frac{5(\sqrt{13} + 2 \sqrt{2}) }{5} }$

$\displaystyle \sf{ = \sqrt{13} + 2 \sqrt{2} }$

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