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: 205
- 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 24 m 0.8 m and 0.5 m. What will be the volume of a chest in the shape of a cube with the same surface area? - Two cubes 3 Two cubes modeled from plasticine have single-digit integer edge lengths with a difference of 1 cm. Can one large cube with an integer edge length be modeled from the same amount of plasticine?
- Box
A paper box is in the shape of a cube. 2,400 cm² of paper was used to make it. Bends for gluing the walls are not included. 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 body 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 wall 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.
- 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. - Number power square
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Block volume height The block has a length of 12 cm and a width of 0.6 dm. The height is the same size as the edge of a cube whose volume is 64cm³. Calculate the volume of the cuboid in cm³.
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