Question

decide if each number is a perfect square, a perfect cube, or neither.
perfect square perfect cube neither
49

Explanation:

Step1: Recall perfect square definition

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

Step2: Check if 49 is a perfect square

We know that \( 7\times7 = 49 \), which can be written as \( 7^2 = 49 \).

Step3: Check if 49 is a perfect cube

A perfect cube is \( n^3 \). Let's test integers: \( 3^3 = 27 \), \( 4^3 = 64 \). Since 49 is between 27 and 64 and not a cube of an integer, it's not a perfect cube.

Answer:

perfect square (because \( 7^2 = 49 \), so 49 is a perfect square and not a perfect cube)