Question

Rationalize the denominator and simplify √5-√3/√5+√3​

Answer 1

Answer:4-√15

Step-by-step explanation:

√5-√3/√5+√3  

=> Rationalize the denominator by multiplying both terms into √5-√3

=(√5-√3)*(√5-√3)/(5+√3)*(√5-√3)

=(√5-√3)^2/ 5-3

=5+3-2√15/2

=8-2√15/2

Simplify:

=4-√15

Answer 2

$\frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ = \frac{ (\sqrt{5} - \sqrt{3}) ^{2} }{ { (\sqrt{5} )}^{2} - ( \sqrt{3}) ^{2} } \\ = \frac{( { \sqrt{5} ) }^{2} + (\sqrt{3} ) ^{2} - 2 (\sqrt{5} )( \sqrt{3}) }{5 - 3} \\ = \frac{5 + 3 - 2 \sqrt{15} }{2} \\ = \frac{8 - 2 \sqrt{15} }{2} \\ = 4 - \sqrt{15}$