Yes.
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20 squared is 400 which is a rational number
No, it is a rational number, because all natural numbers are rational.
No.
The square root of 20 is an irrational number
No, it is a rational number. Numbers in the form of a/b, where a and b are integers, are called rational numbers. 0.666... can be written as 20/3. So it is a rational number.