1. Circle true or false for each statement. \( \begin{array}{l}\text { a. true / false A perfect square may be negative. } \\ \begin{array}{l}\text { b. true / false } \\ \text { c. true / false perfect cube may be negative. } \\ \text { d. true / false }\end{array}\end{array} \begin{array}{l}\text { The square root of a negative number does not exist. }\end{array} \)

A perfect square is defined as a number that can be expressed as the square of an integer. Since squaring any real number (positive or negative) results in a non-negative number, it's impossible for a perfect square to be negative. Therefore, statement (a) is false. When it comes to perfect cubes, any integer can be cubed, and this includes negative numbers. For example, \((-2)^3 = -8\). Thus, a perfect cube can indeed be negative, making statement (c) true. As for the square root of a negative number, in the realm of real numbers, it does not exist; however, in the field of complex numbers, it can be expressed using 'i' (the imaginary unit). Hence, the statement is true if considering only real numbers.