square roots

"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