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October 18th, 2016, 08:38 AM  #1 
Newbie Joined: Oct 2016 From: Minna Posts: 8 Thanks: 0  Evaluation of surds
Evaluate (1+√2÷√5+√3)+(1√2÷√5√3)

October 18th, 2016, 10:52 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,611 Thanks: 1295  Quote:
$\dfrac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}} + \dfrac{1\sqrt{2}}{\sqrt{5}\sqrt{3}}$ common denominator is $(\sqrt{5}+\sqrt{3})(\sqrt{5}\sqrt{3})$ ... $\dfrac{(1+\sqrt{2})(\sqrt{5}\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}\sqrt{3})} + \dfrac{(1\sqrt{2})(\sqrt{5}+\sqrt{3})}{(\sqrt{5}\sqrt{3})(\sqrt{5}+\sqrt{3})}$ can you take it from here?  
October 19th, 2016, 01:15 AM  #3 
Newbie Joined: Oct 2016 From: Minna Posts: 8 Thanks: 0 
pls don't be offended, expand further

October 19th, 2016, 01:43 AM  #4 
Member Joined: Sep 2016 From: India Posts: 88 Thanks: 30 
$\dfrac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\dfrac{1\sqrt{2}}{\sqrt{5}\sqrt{3}}$ $=\dfrac{(1+\sqrt{2})(\sqrt{5}\sqrt{3})+(1\sqrt{2})(\sqrt{5}+\sqrt{3})}{(\sqrt{5}+\sqrt{3})( \sqrt{5}\sqrt{3})}$ $=\dfrac{(1+\sqrt{2})(\sqrt{5}\sqrt{3})+(1\sqrt{2})(\sqrt{5}+\sqrt{3})}{(\sqrt{5})^2(\sqrt{3})^2}$ $=\dfrac{(1+\sqrt{2})(\sqrt{5}\sqrt{3})+(1\sqrt{2})(\sqrt{5}+\sqrt{3})}{53}$ $=\dfrac{\sqrt{5}\sqrt{\not3}+\sqrt{\not10}\sqrt{6}+\sqrt{5}+\sqrt{\not3}\sqrt{\not10}\sqrt{6}}{2}$ $=\dfrac{2\sqrt{5}2\sqrt{6}}{2}$ $=\sqrt{5}\sqrt{6}$ Last edited by deesuwalka; October 19th, 2016 at 01:53 AM. 
October 19th, 2016, 02:24 AM  #5 
Newbie Joined: Oct 2016 From: Minna Posts: 8 Thanks: 0 
Express 148√60÷6√2010√12 in the form a√b+6√3; where a & b are irrational numbers.

October 19th, 2016, 03:46 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,611 Thanks: 1295  
October 19th, 2016, 04:41 AM  #7  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,570 Thanks: 613 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
(148√60)÷(6√2010√12) The first step is to rationalize the denominator. The conjugate expression to 6√2010√12 is 6√20+10√12. Multiply the top and bottom of the original expression and see where it leads. Dan  
October 19th, 2016, 07:40 AM  #8 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  

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