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b) Suppose Jenny divides the square root of her favorite positive integer by $\sqrt2$. Does she have to get an integer? (Remember, when Jenny multiplies the square root of her favorite integer by $\sqrt2$, she gets an integer.)

 Dec 10, 2020
 #1
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It depends upon what  her favorite integer might  be

 

Ex:

 

If it is 8  we  have   sqrt (8)  / sqrt (2) =  sqrt (4)  = 2

 

But......suppose it is 12

 

sqrt (12) /sqrt(2)   =  sqrt (6)    not an integer

 

 

cool cool cool

 Dec 10, 2020
 #2
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Yes, but ONLY if her favorite number is of this form:

 

a(n) =2n^2. So, for numbers 1, 2, 3, 4, 5, 6, 7, 8,9, 10............etc

 

2*1^2 =2,    2*2^2=8,    2*3^2=18,    2*4^2 =32,    2*5^2=50............and so on.

 Dec 10, 2020

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