Login

simplify: 1/ ( root3 + root2 - root5)

$\frac{1}{\sqrt{3} + \sqrt{2} - \sqrt{5}} = \frac{1}{(\sqrt{3} + \sqrt{2}) - (\sqrt{5})} \times \frac{(\sqrt{3} + \sqrt{2}) + (\sqrt{5})}{(\sqrt{3} + \sqrt{2}) + (\sqrt{5})} = \frac{(\sqrt{3} + \sqrt{2}) + (\sqrt{5})}{{(\sqrt{3} + \sqrt{2})}^{2} - {(\sqrt{5})}^{2}} = \frac{(\sqrt{3} + \sqrt{2}) + (\sqrt{5})}{3 + 2 + 2 \sqrt{6} - \sqrt{5}} = \frac{\sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} = \frac{\sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{(\sqrt{3} + \sqrt{2} + \sqrt{5}) \sqrt{6}}{12} = \frac{(\sqrt{18} + \sqrt{12} + \sqrt{30})}{12} = \frac{(3 \sqrt{2} + 2 \sqrt{3} + \sqrt{30})}{12} = \frac{\sqrt{2}}{4} + \frac{\sqrt{3}}{6} + \frac{\sqrt{30}}{12} H e n c e, \frac{1}{\sqrt{3} + \sqrt{2} - \sqrt{5}} = \frac{\sqrt{2}}{4} + \frac{\sqrt{3}}{6} + \frac{\sqrt{30}}{12}$

10

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?