Simplify: (i) √5+√3√5−√3+√5−√3√5+√3 (ii) 12+√3+2

1.	Simplify: (i) √5+√3√5−√3+√5−√3√5+√3 (ii) 12+√3+2√5−√3+12−√5 (iii) 2√5+√3+1√3+√2−3√5+√2
Answer» Simplify: (i) $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} + \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ (ii) $\frac{1}{2 + \sqrt{3}} + \frac{2}{\sqrt{5} - \sqrt{3}} + \frac{1}{2 - \sqrt{5}}$ (iii) $\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} - \frac{3}{\sqrt{5} + \sqrt{2}}$

Simplify: (i) √5+√3√5−√3+√5−√3√5+√3 (ii) 12+√3+2√5−√3+12−√5 (iii) 2√5+√3+1√3+√2−3√5+√2

Answer»

Simplify:

(i) $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} + \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$

(ii) $\frac{1}{2 + \sqrt{3}} + \frac{2}{\sqrt{5} - \sqrt{3}} + \frac{1}{2 - \sqrt{5}}$

(iii) $\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} - \frac{3}{\sqrt{5} + \sqrt{2}}$