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The quantity \(\sqrt{45} - 2\sqrt{5} + \frac{\sqrt{360}}{\sqrt{2}}\) can be expressed as sqrtN, where $N$ is an integer. Find $N$.

 Jul 11, 2020
 #1
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Just do term by term on your calculator:

 

1 - sqrt(45 ) =6.7082039......

 

2 - 2*sqrt(5) = 4.472135955......

 

3 - Sqrt(360) / sqrt(2) =13.4164078.....

 

4 - [6.7082039......  -  4.472135955......  + 13.4164078..... = 15.65247584... This number is the square root of N.

 

5 - All you do is to square the result in 4: 15.65247584^2 =245 - which is your N. Simple, right?

 Jul 11, 2020
 #2
avatar+26007 
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Here is a scan solving w/out a calculator:

 

 Jul 11, 2020

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