Exploring Perfect Squares and Cubes

This video tutorial explores the concepts of perfect squares, perfect cubes, and their roots. It begins with an introduction to perfect squares, explaining their properties and how to find their square roots. The tutorial then moves on to perfect cubes, discussing their volume and cube roots. The syntax of roots, including the radical sign, radicant, index, and coefficient, is explained. Examples are provided to demonstrate finding the square root of 1296 and the cube root of 1728. Finally, the video covers calculating the surface area of a cube given its volume.

What is a perfect square?

• A four-sided figure with all sides equal and 90-degree angles

• A four-sided figure with opposite sides equal

• A three-sided figure with all sides equal

• A figure with no equal sides

What is the square root of 4 cm²?

• 1 cm

• 2 cm

• 4 cm

• 3 cm

What is the value of 3 squared?

• 6

• 9

• 12

• 15

What is the volume of a perfect cube with sides of 2 cm?

• 4 cm³

• 6 cm³

• 10 cm³

• 8 cm³

What is the cube root of 27 cm³?

• 2 cm

• 3 cm

• 4 cm

• 5 cm

What is the radicand in the expression √25?

• 2

• 5

• None of the above

• 25

What is the square root of 1296?

• 34

• 37

• 35

• 36

What is the cube root of 1728?

• 10

• 13

• 11

• 12

If a cube has a volume of 4913 cubic inches, what is the length of one side?

• 17 inches

• 15 inches

• 18 inches

• 16 inches

What is the surface area of a cube with sides of 17 inches?

• 1734 inches²

• 2034 inches²

• 1934 inches²

• 1834 inches²