Question

Which sum is irrational?
A.2/5+3sqrt27
B.4pwr6+49sqrt1/2

Answer 1

square root of a number is, in general, irrational
the exception is if the number is a perfect square. example:4
where sqrt(4)= 2 and that is rational. but sqrt(3) is irrational because 3 is not a perfect square. Most numbers are not perfect squares

Answer 2

yes, \(\large\color{black}{ \displaystyle \sqrt{27} }\) is irrational... so no matter how many other rational numbers you add to it, the sum will still be irrational.