Roots in Geometry: Squares, Cubes, and Exponents

A square garden has an area of 144 square meters. What is the length of one side of the garden?

• 16 meters

• 12 meters

• 10 meters

• 14 meters

A cube-shaped box has a volume of 125 cubic centimeters. What is the length of one edge of the box?

• 10 centimeters

• 5 centimeters

• 7 centimeters

• 3 centimeters

The area of a square playground is 256 square feet. How long is each side of the playground?

• 12 feet

• 14 feet

• 16 feet

• 20 feet

A storage unit is in the shape of a cube with a volume of 729 cubic feet. What is the length of one side of the unit?

• 10 feet

• 9 feet

• 12 feet

• 8 feet

A square tile has an area of 64 square inches. What is the length of one side of the tile?

• 12 inches

• 8 inches

• 6 inches

• 10 inches

A cube has a volume of 1,000 cubic meters. If you want to paint all six faces of the cube, what is the total area you need to paint?

• 500 m²

• 600 m²

• 300 m²

• 1,200 m²

The area of a square field is 1,024 square yards. How many yards long is each side of the field?

• 16 yards

• 32 yards

• 64 yards

• 24 yards

A cube has a side length of 4 meters. What is the volume of the cube?

• 80 cubic meters

• 48 cubic meters

• 64 cubic meters

• 32 cubic meters

If the side length of a square is doubled, how does the area change? Explain using square roots.

• The area increases by a factor of 4.

• The area increases by a factor of 8.

• The area decreases by a factor of 2.

• The area remains the same.

A cube has a volume of 512 cubic inches. What is the length of one side of the cube, and how does this relate to the properties of exponents?

• 10 inches

• 12 inches

• 6 inches

• 8 inches