Square Root Symbol

The square root symbol or square root sign is a mathematical symbol, denoted by ‘√’. This symbol is known as radical, in words. In Maths, you may have learned about different kinds of symbols, which are used to perform arithmetic operations. The root symbol (√ ) is used to represent the square root of any number.

For example, the square root of 2 is represented by √2. Similarly, for other natural numbers, such as 5, 6, 7, 8, 10, etc. we can denote the square roots for them as √5, √6, √7, √8, and √10, respectively. This symbol always denotes the positive square root.

Radicand: The symbol for square root is called radical whereas the number present under the root is called the radicand. Hence, in the above-specified examples, 2, 5, 6, 7, 8, 10 are the radicands.

Basically square root is used to find the number which when multiplied by itself gives the original number, present under the root. Let us understand it by an example. If we multiply 3 by 3, then we get 9, such as 3 x 3 = 9. Now, if we take the root of 9, √9, it will be again equal to 3, i.e. √9 = 3.

Root Symbol (in Word)

The square root symbol in words is said to be a ‘radical’. Or we can say a radical symbol (√ ) is used to represent the square root of any natural number.

Square root formula: The formula to find the square root is:

y = √a

Or

y2 = a

Basically we use the prime factorisation method to find the square root of any number.

Example: 100 = 2 x 2 x 5 x 5

We can see here two pairs of 2 and 5.

√100 = √(2 x 2 x 5 x 5)

By taking out the numbers in pairs, we get:

√100 = 2 x 5 = 10

Recheck: If √100 = 10, then 10 multiplied by 10 should give 100.

Hence, 10 x 10 = 100

Another method to find the square root is by using long division method. This method is used when we cannot apply prime factorisation for large numbers or the number under the root symbol is imperfect square.

List of Square Roots:

Below is the list of the square roots of some numbers which students can use to solve the problems based on it.

Number

Square Root(√)

1

1

2

1.414

3

1.732

4

2.000

5

2.236

6

2.449

7

2.646

8

2.828

9

3

10

3.162

11

3.317

12

3.464

13

3.606

14

3.742

15

3.873

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