The square of any rational number is also rational.
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28 squared is 784 which is a rational number
20 squared is 400 which is a rational number
It would simply be the irrational square root of a rational number. There is no special name for it.
No because pi still remains as an irrational when squared.
5.7 squared is 32.49 and 5.72 squared is 32.7184. Therefore the square root of number between 32.49 and 32.7184 is between 5.7 and 5.72 and probably irrational. One example is the square root of 32.6 which is about 5.70964...