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The product $(3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})$ can be expressed in the form $a+b\sqrt{5}$, where $a$ and $b$ are integers. Find $a+b$.

 Jun 10, 2024
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\((3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5}) \)

 

First two products =  7 -sqrt 5

 

So (7 -sqrt 5) (1 + 6sqrt 5)  =

 

7 -sqrt 5 + 42sqrt 5 - 6*5  =

 

-23  + 41sqrt 5

 

a + b =   18

 

cool cool cool

 Jun 10, 2024

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