Second power - 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: 603
- 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. - Surface = volume
If the volume and the surface area of a sphere are numerically equal, find its radius. - GP - terms
Which term of the geometric progression 2, 8, 32, … is 131,072? - 765 chairs
765 chairs are to be arranged in rows such that the number of chairs in each row equals the number of rows. How many chairs need to be removed to complete this arrangement? - The sum 51 The sum of two numbers is 100 and their difference is 37. Find the difference between their squares.
- Square lawn
A square lawn has a 2 m wide path surrounding it. If the area of the path is 136 square meters, find the area of the lawn. - Difference of squares If the difference between two numbers is 3 and the difference of their squares is 39, then find the larger number.
- Three cubes
Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm, respectively, are melted and formed into a single cube. Find the edge of the new cube. - Selling cloth
By selling 33 m of cloth, a shopkeeper loses an amount equal to the selling price of 3 m of cloth. Find the gain or loss percentage. - 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. - Two points
M and N are two points on the X-axis and Y-axis, respectively. Point P (3, 2) divides the line segment MN in a ratio of 2:3. Find: (i) the coordinates of M and N (ii) slope of the line MN. - Two workers 10
Worker P can do a work 3 times faster than Q and therefore takes 40 days less than Q.Find the time in which P and Q can complete the work individually. - A student 8
A student was asked to write 25 * 9² . By mistake he write 2592. Find the difference. - LS and y-axis intersection In what ratio is the line segment joining P (5, 3) and Q (–5, 3) divided by the y-axis? Also, find the coordinates of the intersection point.
- The product 15
The product of two consecutive even numbers is 48. If the square of the smaller number is 35, what is the other number? - A pattern
If I have a pattern that starts with 1, 4, 9, 16, 25... and so on, which of the following numbers would not appear? - Grain storage
On their farm, Adam's family maintains a storage facility that can hold 19.2 cubic yards (yd3) of grain. Since 1 yard is approximately equal to 0.9144 m, this volume can be converted to m³. - Evaluation order quiz
Which of the following is NOT true about the expression given below? (10 +4)²- 25 ... - Two numbers 17
The sum of two numbers is 9, and the sum of their cubes is 189; find the sum of their squares. - Fraction function
If Begin equation . . . y equals . . . begin fraction . . . x raised to the second power minus 3 times x plus 10 . . . over . . . x plus 4 . . . end fraction . . . end equation, find f(5).
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