How to Find Square Roots and Cube Roots?
Concept
Square root of a number is an inverse operation of squaring a number. The Square of a number is the value of power 2 of the number, while the square root of a number is the number that we need to multiply by itself to get the original number. If ‘a‘ is the square root of ‘b‘, it means that a × a = b. The square of any number is always a positive number, so every number has two square roots, one positive value, and one negative value. For example, both 2 and -2 are square roots of 4.
Whenever a number (x) is multiplied three times, then the resultant number is known as the cube of that number. Thus, the cube for the number (x) becomes x3 or x-cubed. While on the other hand, the cube root of a number is the reverse process of the cube of a number and is denoted by ∛.
Rules
A square root of a number is one of its two equal factors.
A cube root of a number is one of its three equal factors.
Example
The area of a floor in a square room is 121 m2. Find the length of one side of the room.
Solution
s2 = 121
√s2 = √121
s = ±11
s = 11
The length of one side of the room is 11 meters.
Practice How to Find Square Roots and Cube Roots
Practice Problem 1
Evaluate.
√(36)
Practice Problem 2
Evaluate.
∛216
Practice Problem 3
The area of a square post-it note is 64 cm2. Find the length of a side of the post-it.
Practice Problem 4
A giant fish tank in the shape of a cube has a volume of 64 m3. Find the length of one side of the fish tank.
Square of a number: A square number is a number multiplied by itself.
Cube of a number: A cube number is a number multiplied by itself 3 times.
Square Root: One of the two equal factors of a number. If a2 = b, then a is the square root of b.
Cube Root: One of the three equal factors of a number. If a3 = b, then a is the cube root of b.
Radical Symbol: A symbol used to indicate a positive square root √
Pre-requisite Skills
Evaluate exponents
Powers and Exponents
Negative Exponents
Related Skills
Scientific Notation
Computing with Scientific Notation