maths Maths Puzzle

If x is a positive rational number, show that xx is irrational unless x is an integer.

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maths Other Question

What is the 1000th digit to the right of the decimal point in the decimal representation of (1 + root 2)3000 ? A rhombus, ABCD, has sides of length 10. A circle with center A passes through C (the opposite vertex.) Likewise, a circle with center B passes through D. If the two circles are tangent to each other, what is the area of the rhombus?