Square root - practice problems
Roots in math refer to values that satisfy an equation when set to zero (e.g., x = 2 is a root of x2 - 4 = 0 ).The square root (√) of a number a is a value x such that x2 = a (e.g., √25 = 5 ).
Higher-order roots, like cube roots (cbrt or ∛), solve equations such as x3 = 8 (result: x = 2 ).
Roots are fundamental in algebra, calculus, and real-world applications like physics (e.g., calculating distances or growth rates).
Number of problems found: 1402
- A ladder 3
A 30 foot ladder is set against the side of a house so that it reaches up 24 feet. If Elizabeth grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? Round to the nearest tenth - 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. - 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. - 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. - 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. - 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?
- The rhombus (a,d) Find the area of a rhombus, one side of which measures 20 cm and one diagonal of which is 24 cm.
- A tree 3
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground at an angle of 30°. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the original height of the tree. - A field
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m and whose non-parallel sides are 14 m and 13 m. Find the area of the field. - Triangle 90
A triangle has sides of 6 cm, 4.5 cm, and 7.5 cm. What are the sizes of its angles? - 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? - A baseball
A baseball is hit over a fence that is 325 feet away and 110 feet tall. How far did the ball travel in a straight line when it reached the fence? - Three inscribed objects
A circle is inscribed in a square. An equilateral triangle with side 4√3 is inscribed in that circle. Find the length of the diagonal of the square. - A variable
A variable rectangle has a constant area of 35 cm². Find the side lengths when the perimeter is at its minimum.
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