Square (second power, quadratic) + prime numbers - practice problems - page 2 of 3
Number of problems found: 48
- The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets and their products was the power of the prime number. Find all possible ticket prices. - Two gears
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM - Cutting paper
Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square. - Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
- Dimensions 7131
The paper has dimensions 220mm and 308mm. We need to cut it into as large a square as possible. What will be the side of this square? - Two rectangles
I cut out two rectangles with 54 cm² and 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together, I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your - Glass panel
A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut? - Cuboid walls
Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm². - Pagans
Elena cut out the same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagan occupied 28.26 cm² of the bottom of the sh
- Rectangular 4819
Divide the rectangular meadow with dimensions of 1280m and 320m into a square shepherd with the longest possible side of the square. How many square pastures did you divide the meadow? - Two-digit 4750
My number for today: the product of the square of the smallest prime number with the smallest two-digit prime number - Expression 4451
Find the largest natural number d that has that property for any natural number the number n is the value of the expression V (n) = n ^ 4 + 11n²−12 is divisible by d. - Rectangular 4402
Our task is to save the rectangular images with dimensions of 105 mm and 42 mm so that we cover the smallest square. What will be its size, and how many pictures do we need? - Maximally 4036
Mr. Novák wants to pave the terrace with tiles of two sizes to be as small as possible. Its terrace is square with a side 3 meters long. There is a wall of the house on two sides of the terrace. Next to the wall, he wants to put small tiles, the rest larg
- Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - Tiles
How many tiles of 20 cm and 30 cm can build a square if we have a maximum of 100 tiles? - Square tiles
The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor. - Mr. Zucchini
Mr. Zucchini had a rectangular garden whose perimeter was 28 meters. The garden's area filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and write n - Primes 2
For what primes p,q,r is true: p²-(q+r)²=647
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