Square Root And Cube Root

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.

NUMBER SQUARE SQUARE ROOT
1 1 1.000
2 4 1.414
3 9 1.732
4 16 2.000
5 25 2.236
6 36 2.449
7 49 2.646
8 64 2.828
9 81 3.000
10 100 3.162
11 121 3.317
12 144 3.464
Number Cube Cube root
1 1 1.000
2 8 1.260
3 27 1.442
4 64 1.587
5 125 1.710
6 216 1.817
7 343 1.913
8 512 2.000
9 729 2.080
10 1000 2.154
11 1331 2.224
12 1728 2.289
13 2197 2.351
14 2744 2.410
15 3375 2.466

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.

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