Which one of the following is not a real number?

To decide which value is not a real number, recall that real numbers include every rational and irrational number that can be placed on the number line, while the square root of a negative number is imaginary (it uses the imaginary unit i, where i = √-1).

Check each option: π is irrational and real; 1/√2 is irrational and real; -(1/3)^(1/2) is the negative square root of one-third, a negative irrational number, and so it is also real.

Only √−4 takes the square root of a negative number. √−4 = √4 × √−1 = 2i, an imaginary number that does not lie on the real number line. Therefore √−4 is the value that is not a real number, and it is the correct choice.