Exploring Perfect Squares and Cubes

What is a perfect square?

• A number that is the product of three equal factors

• A number that is the product of two equal factors

• A number that can be divided by 2

• A number that is a prime number

Which of the following is a perfect cube?

• 49

• 36

• 27

• 16

What is the prime factorization of 36?

• 2 x 2 x 3 x 3

• 3 x 3 x 3 x 3

• 2 x 3 x 3 x 3

• 2 x 2 x 2 x 3

How can you determine if a number is a perfect square using prime factorization?

• By checking if it can be divided by 3

• By making two equal groups of its prime factors

• By making three equal groups of its prime factors

• By checking if it can be divided by 2

What is the square root of 1296?

• 24

• 48

• 32

• 36

Which of the following numbers is a perfect cube?

• 1000

• 1024

• 1444

• 1296

What is the cube root of 1728?

• 13

• 10

• 11

• 12

How can you determine if a number is a perfect cube using prime factorization?

• By checking if it can be divided by 2

• By making two equal groups of its prime factors

• By making three equal groups of its prime factors

• By checking if it can be divided by 3

What is the volume of a cube with a side length of 15 cm?

• 2250 cm²

• 3375 cm²

• 2250 cm³

• 3375 cm³

How do you calculate the surface area of a cube?

• 6 times the volume

• 6 times the side length

• 6 times the side length squared

• 6 times the side length cubed