Solve the equation:

x2 = 81

How many solutions are there for x?

Solve the equation:
x3 = 27

How many solutions are there for x?
The 51 is in between what 2 perfect squares?


The 3300 is in between what 2 perfect cubes?
The volume of a cube is 64 blocks. What is the length of one side of the cube? Show an equation and solve it.

1 answer

1. For x^2 = 81, there are two possible solutions: x = 9 or x = -9.

2. For x^3 = 27, there is only one solution: x = 3.

3. 51 is in between the perfect squares 49 and 64 (7^2 and 8^2).

4. 3300 is in between the perfect cubes 27 and 64 (3^3 and 4^3).

5. Let s be the length of one side of the cube. The volume of a cube is given by s^3 = 64. Solving for s, we get s = ∛64 = 4. Therefore, the length of one side of the cube is 4 blocks.