Question

Root 5 +root 3 / root 5 - root 3 = a+b root 3

Answer 1

5√3
I hope you understand

Answer 2

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

$rationalize \: \sqrt{5} + \sqrt{3}$

$\sqrt{5 } + \sqrt{3} \times \sqrt{5} + \sqrt{3} \div \sqrt{5 } - \sqrt{3} \times \sqrt{5} + \sqrt{3} = a + b \sqrt{3}$

$( \sqrt{5} ) {}^{2} + (\sqrt{3} ) {}^{2} + 2 \sqrt{5 } \times \sqrt{3} \div (\sqrt{5} ) {}^{2} - ( \sqrt{3} ) {}^{2}$

$5 + 3 + 2 \sqrt{15} \div 5 - 3 = a + b \sqrt{3}$

$8 + 2 \sqrt{15} \div 2 = a + b \sqrt{3}$

$8 \div 2 + 2 \sqrt{15} \div 2 = a + b \sqrt{3}$

$4 + \sqrt{15} = a + b \sqrt{3}$

$compare$

$a = 4$

$b \sqrt{3} = \sqrt{15}$

$b = \sqrt{15} \div \sqrt{3}$

$b = 15 \frac{1}{2 } \div 3 \frac{1}{2}$

$b =( 15 \div 3) \frac{1}{2}$

$b = 5 \frac{1}{2}$

$b = \sqrt{5}$