Question

State if each number is Rational,Irrational,or not a real number?
1.)square root of 9/16
2.) square root of -9
3.)square root of -16 divided by -4
4.)square root of -8(-2)
5.)square root of 25 divided by 8
6.)square root of -1/4

Please Help! I have been sick for 4 weeks and I still don't get this assignment.

Answer 1

the smallest set is the natural numbers: 1,2,3,...
Next is whole numbers: 0,1,2,3,4...
Next is integers: ...-2,-1,0,1,2,...
Next is rational: these are all the fractions 1/2, 3/7, and so on
Next is irrational: everything else
Real numbers include all of the above
Finally there are the complex numbers which include all the real numbers, as well as imaginary ones

√(9/16) = √9/√16 = 3/4: rational
√-9 = √9√-1 = 3i: not real (complex)
√(-16/-4) = √4 = 2: rational
√-16/-4 = 4i/4 = i: not real
√((-8)(-2)) = √16 = 4: rational
(√-8)(-2) = 2√2 i (-2) = -4√2i: not real
√25/8 = 5/8: rational
√(-1/4) = (√-1)/2 = -1/2 i: not real

As you can see above, it is necessary to use parentheses sometimes, to make it clear just what you mean.