Question

Which of the following statements are true? a) 49 is a perfect square b) 2197 is both a perfect square and perfect cube c) 125 is a perfect cube d) 25 is a perfect cube e) 21 is neither a perfect square nor cube?

1) 49 is a perfect square
2) 2197 is both a perfect square and perfect cube
3) 125 is a perfect cube
4) 25 is a perfect cube
5) 21 is neither a perfect square nor cube

Answer 1

True statements are that 49 is a perfect square, 2197 is both a perfect square and perfect cube, 125 is a perfect cube, and 21 is neither a perfect square nor cube. The statement that 25 is a perfect cube is false.

Step-by-step explanation:

Let's evaluate each statement:

1. 49 is a perfect square because 7 x 7 = 49.
2. 2197 is both a perfect square and perfect cube; indeed, it is 134, which also makes it a square of 132 (169) and a cube of 13.
3. 125 is a perfect cube, as 5 x 5 x 5 = 125.
4. 25 is not a perfect cube; a perfect cube would be a number like 8 (2 x 2 x 2) or 27 (3 x 3 x 3), which are cube numbers because they can be expressed as some integer to the third power.
5. 21 is neither a perfect square nor cube; the closest perfect square is 16 (4 x 4) and the closest cube is 27 (3 x 3 x 3).

As such, the true statements are:

• 49 is a perfect square.
• 2197 is both a perfect square and a perfect cube.
• 125 is a perfect cube.
• 21 is neither a perfect square nor a cube.