headache again..

1. Prove that the product of 4 successive integers is not a perfect square.
2. Simplyfy [1+n(n+1)(n+2)(n+3)]^1/2
3. Find a 100-digits number N, with no digit 0, which is divisible by it's sum of digits.
4. Supposedly a rectangle, 5 x 13, is cut into 4 portions, namely A, B, C, and D.

Then the 4 portions are joined to become a square, 8 x 8.

Now find the area of the rectangle and the square. What?
Do note that these 2 are made up of identical pieces.
5. Given a straight line, abc, as shown. Find the ratio ac/ab, which is the same as ab/bc.
Actually, the 4th and 5th is quoted from a book, The Golden Ratio by Mario Livio. It is interesting.
I need help..