No because it can be expressed as a fraction in the form of 30/1
The expression "30 to the square root" is not clearly defined, but if you mean (30^{\sqrt{30}}), then this expression is irrational because it involves raising a rational number (30) to an irrational exponent ((\sqrt{30})). In general, a rational number raised to an irrational power results in an irrational number. Hence, (30^{\sqrt{30}}) is irrational.
Rational
Cos(30) = sqrt(3)/2 = 0.866025403.... ( Which is irrational).
The square root of (any number that isn't a perfect square) is irrational.
Because it can't be expressed as a fraction
An irrational number.
No because the square root of 900 is 30 which is a rational number
The sum of a rational and irrational number must be an irrational number.
No. The sum of an irrational number and any other [real] number is irrational.
irrational
A rational number is any number that does not have an infinite number of digits. So, as you wrote it, 2.8333333 is a rational number. However, if you meant the 3s to go on forever (as in the number 2.8 + 1/30), that would be an irrational number.
No, 3.56 is not an irrational number. 3.56 is rational.