Question

(1/√2+√3)+(2/√3+2)+(3/2+√5)

Answer 1

Answer:

9.32992610463

Step-by-step explanation:

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Answer 2

Answer:

$3\sqrt{5}-2-\sqrt{2} -\sqrt{3}$  

Step-by-step explanation:

$= \frac{1}{\sqrt{2}+\sqrt{3}}+\frac{2}{\sqrt{3}+2}+\frac{3}{2+\sqrt{5}}\\\\= (\frac{1}{\sqrt{2}+\sqrt{3}}*\frac{{\sqrt{2}-\sqrt{3}}}{{\sqrt{2}-\sqrt{3}}}) +(\frac{2}{\sqrt{3}+2}*\frac{{\sqrt{3}-2}}{{\sqrt{3}-2}})+(\frac{3}{2+\sqrt{5}}*\frac{2-\sqrt{5}}{2-\sqrt{5}})\\\\= \frac{\sqrt{2}-\sqrt{3}}{(\sqrt{2})^2-(\sqrt{3})^2} + \frac{2\sqrt{3} - 4 }{({\sqrt{3})^2-(2)^2}} +\frac{6 - 3\sqrt{5} }{(2)^2 - (\sqrt{5})^2 }$

$= \frac{\sqrt{2}-\sqrt{3}}{2-3} + \frac{2\sqrt{3} - 4 }{3-4} +\frac{6 - 3\sqrt{5} }{4 - 5 }\\\\= \frac{\sqrt{2}-\sqrt{3}}{-1} + \frac{2\sqrt{3} - 4 }{-1} +\frac{6 - 3\sqrt{5} }{-1}\\\\= \frac{(\sqrt{2}-\sqrt{3})+ (2\sqrt{3} - 4) +(6 - 3\sqrt{5})}{-1}\\\\= \frac{\sqrt{2}-\sqrt{3}+ 2\sqrt{3} - 4 +6 - 3\sqrt{5}}{-1}\\\\= \frac{\sqrt{2}+\sqrt{3}+2-3\sqrt{5}}{-1}\\\\= \frac{2+\sqrt{2}+\sqrt{3}-3\sqrt{5}}{-1}\\\\\\Apply~~the~~fraction~~rule:\frac{-a}{-b}=\frac{a}{b}$

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

if you want in decimal

$= 9.32992610463$

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