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.)
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.
