Perfect Squares
What is the square of 9?
81
What is the square root of 49?
7
In a right triangle, if one leg is 6 units and the hypotenuse is 10 units, what is the length of the other leg?
Using the Pythagorean theorem, the other leg of the right triangle is √(10^2 - 6^2) = √(100 - 36) = √64 = 8 units.
Evaluate: 3³
3³ = 3 x 3 x 3 = 27
Evaluate: ∛27
∛27 = 3
If a square has a side length of 7, what is the area of the square?
49 units squared
Find the value of √81.
9
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).
What is the cube root of 64?
∛64 = 4
Find the value of ∛125.
∛125 = 5
How many perfect squares are there between 1 and 100?
There are 10 perfect squares between 1 and 100 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100).
If the area of a square is 100 square meters, what is the length of one side?
If the area of a square is 100 square meters, the length of one side is √100 = 10 meters.
A ladder is leaning against a wall. If the ladder is 25 feet long and the base is 7 feet away from the wall, how high up the wall does the ladder reach?
Using the Pythagorean theorem, the height up the wall that the ladder reaches is √(25^2 - 7^2) = √(625 - 49) = √576 = 24 feet.
What is the volume of a cube with a side length of 5 units?
The volume of a cube with a side length of 5 units is 5³ = 5 x 5 x 5 = 125 cubic units.
What number when cubed gives a result of 64?
The number that when cubed gives a result of 64 is 4, because 4³ = 64.
Which two perfect squares does 150 fall between?
Evaluate: √196
√196 = 14
In a triangle with sides of length 5, 12, and x, what is the value of x?
Using the Pythagorean theorem, x = √(5^2 + 12^2) = √(25 + 144) = √169 = 13.
Simplify: 5³
5³ = 5 x 5 x 5 = 125
If the volume of a cube is 64 cubic units, what is the length of one side?
If the volume of a cube is 64 cubic units, the length of one side is ∛64 = 4 units.
Which two perfect squares and integers does the square root of 20 fall between?
perfect squares - 16 and 25
integers - 4 and 5
Solve. 2x2 - 4 = 28
x = 4, -4
If the legs of a right triangle are 9 units and 12 units, what is the length of the hypotenuse?
Using the Pythagorean theorem, the length of the hypotenuse is √(9^2 + 12^2) = √(81 + 144) = √225 = 15 units.
Find two consecutive numbers that are perfect cubes.
Two consecutive numbers that are perfect cubes are 1 and 8 (1³ = 1, 2³ = 8).
Solve x3 + 5 = 734
x = 9