There are two aspects to understand here: Square root and Cube roots. To find the square root of any number we need to find a number which when multiplied twice by itself gives the original number.
Example: √4 = √(2 × 2) = 2
To find the cube root of any number we need to find a number which when multiplied three times by itself gives the original number.
Example: ∛27 = ∛(3 × 3 × 3) = 3
Memorizing the squares and the square roots of the first few numbers are almost elementary and it can help you solve problems much faster rather than having to work it out. Following is square roots list of the first 12 numbers and Cube root list of the first 15 numbers.
Square Root and Cube Root Symbol
Let’s understand each concept with an example: If we multiply 5 by itself, we get 25. Now, 5 is the square root of 25 and 25 is the square number. This is also known as a perfect square because it can be represented as the product of two equal integers (5×5). A square root is expressed by the symbol: √
Now, what if the number can’t be expressed as the product of two equal integers? For example, the square root of 48 is 6.92820… Numbers like these are termed as imperfect squares because they are not integers. (They are fractions or decimals instead.)
What happens when you take 3 equal integers and express their product? Well, you get a cube. For example, (5x5x5) = 125. Hence 125 is the cube and 5 is the cube root. The cube root symbol is represented by ∛.
The symbol is almost the same as the square root symbol but the number 3 is denoted on the radical symbol.
Having an app that can effectively demonstrate the concepts in an easy manner is quite beneficial.