Cube root - practice problems
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. It is denoted by the symbol ∛ or as a fractional exponent of 1/3. Unlike square roots, cube roots of negative numbers are real and negative. This operation is essential for solving cubic equations and working with three-dimensional measurements. Students learn both exact cube roots of perfect cubes and approximation methods for other numbers. Cube roots appear frequently in volume calculations, physics formulas, and engineering applications.Number of problems found: 208
- Cbrt of fraction
If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18 26/27. Find the fraction. - Binary series
The 4th term of a G.P. is 16 and the 7th term is 128 . Find the first term and common ratio of the series. - Ones cube
Find the volume of a cube whose total surface area is 6 m². - Geometric 20
Find the geometric mean of 15 15 20 25 30. - Perfect square or cube
Would you classify 324 as a perfect square, perfect cube, both, or neither? ... - A chest made
A chest in the shape of a cuboid made of sheet iron has dimensions of 2.4 m × 0.8 m × 0.5 m. What will be the volume of a cube-shaped chest with the same surface area? - Boxes
Petra has planted flowers in two boxes in the shape of a cube. The first box has an internal dimension of 70 cm and the second 5 dm. She wants to make one box in the shape of a cuboid, into which she could transplant both flowers from these boxes. The new - Two cubes 3 Two cubes made of plasticine have single-digit integer edge lengths differing by 1 cm. Can a single larger cube with an integer edge length be made from the same total amount of plasticine?
- Box
A paper box is in the shape of a cube. 2,400 cm² of paper was used to make it (not including folds for gluing the walls). Calculate the volume of the box. - Original model
When drying, the modeling mass loses 36% of its original volume. If the cube's volume is 5.12 dm³ after drying, what was the original length of the edge? - Cube small diagonal
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and space diagonals. - Paper box volume
The paper box is cube-shaped. 2400 cm² was used for its production. Bends for gluing the walls are omitted. What is the volume of the box? - Cube triangle volume
In the cube ABCDEFGH, the area of triangle ABK is √20 cm². How much cm² is the volume of ABGH in a cube if you know that K is the midpoint of edge CG? - Diagonal of a cube Calculate the volume of a cube with a face diagonal of u = 20 cm.
- Cube surface volume The surface of the cube is 150 dm². Calculate its volume.
- Bacteria hourly increase What % of bacteria will increase hourly if the number increases from 100,000 to 370,000 in 5 hours?
- Inscribed cube A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area.
- Circumscribed - sphere A cube with a volume of 4096 cm³ is described and inscribed by a sphere. Calculate how many times the volume of the circumscribed sphere is greater than the inscribed sphere.
- Jakub 6 Jakub collects dice, all of the same size. Yesterday he found a box into which he began to place the dice. The first layer covered exactly the square bottom of the box. He placed five more layers similarly, but in the middle of the next layer the dice ran
- Cube edge surface
The length of the cube's edge in cm is expressed as a natural number. Its volume is greater than 100 and less than 200. Calculate the surface area of the cube.
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