Question

rationalize root 5 + root 3 by root 5 minus root 3 is equal to a + b root 15​

Answer 1

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

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

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

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

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

$= 4 + \sqrt{15} = a + b \sqrt{15}$

Hence, a = 4

and b = 1