Question

find a rationalize denominator
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Answer 1

HOPE IT HELPS

root 5+root 3/root 5-root 3

(root 5+root 3/root 5-root 3)*root 5+root 3

(root 5+root 3)^2/2

5+3+2 root 15/2

8+2 root 15/2

4+root 15

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Answer 2

$\rm{rationalise \: the \: denominator \: of \: \frac{\sqrt{ 5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }}$

$\implies\rm{ \frac{\sqrt{ 5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }$

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

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

$\implies \rm{\frac{{ {5} + 3 } + 2\sqrt{15} }{ 5 - 3}}$

$\implies \rm{\frac{{ 8} + 2\sqrt{15} }{ 2}}$

$\implies \rm{\frac{{ \cancel{ 2}} (4+ \sqrt{15} ) }{ \cancel{2}}}$

$\fbox{ \therefore{ 4 + \sqrt{15} }}$