Raising to the one half (1/2) power is the same as taking the square root.
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The square root of 48 is a rational or irrational
Yes, it is the principal square root of 4, and it is rational.
It means that it is an exponent, and that it is not a rational number - i.e., one that can be written as a fraction of two integers.
The square root of 2.56 is rational. This is because 2.56 can be expressed as 256/100, which simplifies to 64/25. The square root of 64 is 8 and the square root of 25 is 5, so the square root of 2.56 is 8/5, which is a rational number.