Question

decide if each number is a perfect square, a perfect cube, or neither.
perfect square: 49
perfect cube: 1,000, 8
neither: 15
(the number 16 is to be classified)

Explanation:

Step1: Recall perfect square definition

A perfect square is a number that can be written as \( n^2 \) where \( n \) is an integer.

Step2: Check if 16 is a perfect square

We find an integer \( n \) such that \( n^2 = 16 \). We know that \( 4^2 = 16 \) (since \( 4\times4 = 16 \)).

Step3: Check if 16 is a perfect cube

A perfect cube is a number that can be written as \( m^3 \) where \( m \) is an integer. Let's test integers: \( 2^3 = 8 \), \( 3^3 = 27 \). Since \( 8<16<27 \), there's no integer \( m \) with \( m^3 = 16 \).

Answer:

16 is a perfect square (so it should be placed in the "perfect square" box).