Square Root And Cube Root

There are two aspects to understand here: Squares and Square roots.

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:\(\sqrt{} \)

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 is represented by\( \sqrt[3]{1} \)

The symbol is almost the same as the square root symbol but the number 3 is denoted on the radical symbol.

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.

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

Having an app that can effectively demonstrate the concepts in an easy manner is quite beneficial.


Practise This Question

If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be
[MNR 1978]