Square (second power, quadratic) - practice problems
Squaring a number means multiplying it by itself, raising it to the second power, denoted as n² or n×n. The result is always non-negative for real numbers, creating a parabolic relationship when graphed. Perfect squares are integers that result from squaring whole numbers (1, 4, 9, 16, 25, etc.). Squaring is fundamental to the Pythagorean theorem, area calculations for squares and circles, and the quadratic formula. The inverse operation is taking the square root. Understanding squares is essential for algebra, geometry, and physics, particularly in formulas involving area, distance, and energy.Number of problems found: 3013
- The product 19
The product of two consecutive positive integers is 306. Find the integers. - ABCD rhombus
ABCD is a rhombus with sides of 10.5 cm. If the length of diagonal AC = 15.8 cm, use the cosine rule to: a. calculate the length of diagonal BD to the nearest centimetre, b. find the angles of the rhombus to the nearest degree. - Spherical sector - parameters
Find the volume and surface area of a spherical sector whose base has a height of 8 cm, drawn on a sphere with a diameter of 36 cm. - Insert two > GP
If 4, 36, 324 are in a geometric progression, insert two more numbers into this progression so that it still forms a geometric progression. - The perimeter 13
The perimeter of a rectangle is 22 cm. What are its dimensions if it has the maximum possible area? - Enlarged photo
A photograph has been enlarged by a scale factor of 1.75. If the enlarged photo has an area of 675 cm², what is the area of the original photo? - Isosceles right triangle
If I have a right triangle with each leg on either side of the right angle measuring 24 inches, what is the length of the hypotenuse? - Equilateral RT
In a right triangle, leg a = 12 and leg b = 12. What is the hypotenuse c? - Four plates
Four equal maximum-sized circular plates are cut from a square sheet of paper with an area of 784 cm². Calculate the circumference of each plate. - Square park
Amyra goes for a walk in a square park. The perimeter of the park is 1,235 m. Find the side length of the park. - Area + perimeter TR2
Find the area of a triangle, two sides of which are 8 cm and 11 cm and whose perimeter is 32 cm. - GP - negative term
The first term of a geometric progression is −3 and the square of the second term equals its 4th term. Find the 7th term of the progression. - Eva wraps
Eve wraps a gift box in the shape of a right rectangular prism. The figure shows a net for the gift box. How much wrapping paper did she use, in square metres? - The surface 5
The surface area of a cylinder is 6,140 cm², and the base radius is 25 cm. What is the height? - A rope for cow
Find the length of rope by which a cow must be tethered so that it can graze an area of 154 m². - Parallel lines - dist
Find the distance between the parallel lines 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0. - A person 2
A person has 2 parents, 4 grandparents, 8 great-grandparents, and so on. Find the total number of ancestors during the ten generations preceding his own. - Angle of inclination
Find the angle of inclination of a ramp that rises 80 cm over a horizontal length of 200 cm. - A rectangle 15
A rectangle is 5 cm longer than its width. Its area is 6 cm². What are the dimensions of the rectangle? - Rhombus = area, diagonal
The area of a rhombus is 144 cm². One diagonal is twice the length of the other. How long is the shorter diagonal?
Do you have unsolved math question and you need help? Ask a question, and we will try to solve it. We solve math question.
