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: 1285
- Equilateral RT
On a right triangle, side a is 12, and side b is 12. What is side c?
- Four plates
Four equal maximum sized circular plates are cut off from a square paper sheet of area 784 sq cm. Calculate the circumference of each plates.
- Area + perimeter TR2
Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.
- A rope for cow
Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 154 sq m .
- 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 sq cm. One of its diagonals is twice 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 24 cm.
- A tree 3
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the 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 the non parallel sides are 14 m and 13 m. Find the area of the field.
- Triangle 90
Triangle made by 6 cm 4.5 cm and 7.5 cm. what angles does it make?
- 765 chairs
765 chairs are arranged in rows in such a way that the number of chairs in each row is equal to the number of rows. How many chairs needs to be removed to complete this arrangement?
- A baseball
A baseball is hit over the 325 foot fence, which is 110 feet tall. How far did the ball carry on a straight line when it reached the fence?
- Three inscribed objects
A circle is inscribed in a square. An equilateral triangle of 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 lengths of the sides when the perimeter is minimum.
- A chord 2
A chord of length 16 cm is drawn in a circle of radius 10 cm. Calculate the distance of the chord from the center of the circle.
- Isosceles triangle 17
One of the equal sides of an isosceles triangle is 13 cm and its perimeter is 50 cm. Find the area of the triangle.
- Spheres - ratios
The surface area of two spheres are in the ratio 1 : 4 . Find the ratio of their volumes.
- Two circles 3
Two circles are inscribed in a square whose side is 4 cm. Find the radius of the smaller circle.
- Grassland and goat
An unfenced grassland is a right triangle ABC with AB = 4m, BC = 8m, and AC as hypotenuse. A goat is tied to a 5-m long rope with its stake at point O, which is 2m from side AB and 2m from the prolongation of side BC through corner B. Then: 1. How far is
- A ladder 2
A ladder 10 m long reaches the window of a house 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.
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