Question

rationalize the denominotor:-
√5-√3
√5+√3​

Answer 1

Answer:

➡ 4-√15

Step-by-step explanation:

$\frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

$= \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

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

Now, using identities

(a^2-b^2) and (a-b)^2

$\frac{ { \sqrt{5} }^{2} + { \sqrt{3} }^{2} - 2 \times \sqrt{5} \times \sqrt{3} }{5 - 3}$

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

$= \frac{8 - 2 \sqrt{15} }{2}$

$= 4 - \sqrt{15}$