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

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

UpStudy AI · Accepted Answer

**a.** False  
- For any real number $$ n $$, the square $$ n^2 $$ is nonnegative. Therefore, a perfect square (which is of the form $$ n^2 $$) cannot be negative.

**c.** True  
- The cube of a number can be negative. For example, if $$ n = -2 $$, then $$ n^3 = -8 $$, which is negative. Thus, a perfect cube (of the form $$ n^3 $$) may be negative.

**d.** True  
- In the context of real numbers, the square root of a negative number is not defined because there is no real number $$ n $$ such that $$ n^2 $$ is negative. (Note: In the complex number system, we define $$ \sqrt{-1} = i $$, but the statement is typically considered within the real number system.)
**a.** False **c.** True **d.** True

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