Question

Rationalise
the denominatór
simplity
15-
+ 53
3​

Answer 1

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Answer 2

Step-by-step explanation:

$\sf \dfrac{ \sqrt{5}+ \sqrt{3}}{ \sqrt{5}- \sqrt{3}} \times \dfrac{ \sqrt{5}+ \sqrt{3}}{ \sqrt{5}+ \sqrt{3}}$

$\implies \sf \dfrac{{( \sqrt{5} + \sqrt{3})}^{2}}{{ \sqrt{5}}^{2}- { \sqrt{3}}^{2}}$

$\implies \sf \dfrac{{ \sqrt{5}}^{2}+{ \sqrt{3}}^{2} + 2 \times \sqrt{5} \times \sqrt{3}}{5-3}$

$\implies \sf \dfrac{5+3 + 2 \sqrt{15}}{2}$

$\implies \sf \dfrac{8+2 \sqrt{15}}{2}$

$\implies \sf \dfrac{2(4+ \sqrt{15})}{2}$

$\implies \sf 4+ \sqrt{15}$

Hope it helps