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The quantity sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) can be expressed as sqrtN, where N is an integer. Find N.

 Jul 1, 2021

Best Answer 

 #1
avatar+32658 
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"The quantity sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) can be expressed as sqrtN, where N is an integer. Find N."

 

sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) = sqrt(9*5) + 2*sqrt(5) + sqrt(2*5*36)/sqrt(2)

 

= 3*sqrt(5) + 2*sqrt(5) + sqrt(2)*sqrt(5)*sqrt(36).sqrt(2) 

 

=  3*sqrt(5) + 2*sqrt(5) + 6*sqrt(5) 

 

= 11*sqrt(5)  

 

= sqrt(11^2 * 5) 

 

= sqrt(605)

 

N = 605

 Jul 1, 2021
 #1
avatar+32658 
+2
Best Answer

"The quantity sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) can be expressed as sqrtN, where N is an integer. Find N."

 

sqrt(45) + 2*sqrt(5) + sqrt(360)/sqrt(2) = sqrt(9*5) + 2*sqrt(5) + sqrt(2*5*36)/sqrt(2)

 

= 3*sqrt(5) + 2*sqrt(5) + sqrt(2)*sqrt(5)*sqrt(36).sqrt(2) 

 

=  3*sqrt(5) + 2*sqrt(5) + 6*sqrt(5) 

 

= 11*sqrt(5)  

 

= sqrt(11^2 * 5) 

 

= sqrt(605)

 

N = 605

Alan Jul 1, 2021

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