# Square + cube root - practice problems

#### Number of problems found: 48

- Annual growth

The population has grown from 25,000 to 33,600 in 10 years. Calculate what was the average annual population growth in%? - Derivative problem

The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal. - One third power

Which equation justifies why ten to the one-third power equals the cube root of ten? - Six speeds

A drilling machine is to have 6 speeds ranging from 50 to 750 revolutions per minute. If the speed forms a geometric progression, determine their values. - Three members GP

The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers. - Profit growth

The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods? - Power

Number left(sqrt(14 * sqrt[ 4 ] (14)) right)^{ 17 }can be written in the form 14^x. Find the value of x. - Root

Use law of square roots roots: cbrt (sqrt[2] (sqrt[4] (6))) = sqrt[n] (6) - Pyramid cut

We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm². Find the area of the - Wallpaper

3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide? - Regular square prism

The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism. - Alien ship

The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - Body diagonal

The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Rectangle pool

Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material. - Magnified cube

If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - Cubes

One cube is an inscribed sphere and the other one described. Calculate the difference of volumes of cubes, if the difference of surfaces in 231 cm². - Cube in a sphere

The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Prism X

The prism with the edges of the lengths x cm, 2x cm, and 3x cm has volume 20250 cm³. What is the area of the surface of the prism? - Cone

Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane, if solids have the same volume. - The cube

The cube has a surface area of 216 dm². Calculate: a) the content of one wall, b) edge length, c) cube volume.

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Square practice problems. Cube root - practice problems.