Square Root of 2025

Square root of 2025 is 45. To find the square root of any given number, prime factorisation method, long division method, simplified method and repeated subtraction method can be used. Few methods are mentioned below. 2025 is a perfect square number hence we can determine its square root. 45 is the square root of 2025 as 45 multiplied by 45 gives the number 2025. Interestingly, – 45 × – 45 is also 2025. Hence It is represented as √2025 = 土45.

Refer to the topic Squares and Square roots for all the details.

Note the Following:

  • The Square root of 2025 = √2025 where √ = radical, and 2025 is the radicand.
  • Exponential Form of Square root of 2025 = 20251/2
  • Solution for √2025 = 45
  • Square root of 2025 is Irrational = False

What is the Square root of 2025?

The square root of 2025 is 45. In other words, the square of 45 is 2025. i.e 45 × 45 is 2025. Also – 45 × – 45 is 2025. 

√2025 = 45

How to Find the Square root of 2025?

There are three methods to find the Square root of 2025 

  • Prime Factorisation method
  • Long Division method
  • Repeated Subtraction method

Square root of 2025 by Prime Factorisation Method

As 2025 is a perfect square number, It can be divided continuously by a prime number. Let us start with 3. Continue the division until the remainder becomes 1. The same prime divisors are grouped into 2 ( as this is square root) and the groups are multiplied to get the square root.

The given number, 2025 will be expressed as;

3

2025

3

675

3

225

3

75

5

25

5

5

×

1

2025 = 3 × 3 × 3 × 3 × 5 × 5

Grouping into 2 with same divisors: 

Group 1 = 3 × 3, considering only 3

Group 2 = 3 × 3, considering only 3

Group 3 = 5 × 5, considering only 5

Therefore the square root of 2025 = 3 × 3 × 5 = 45.

Square root of 2025 by Long Division Method

To understand the long division method, follow the below mentioned detailed steps;

Step 1:  Grouping the given number into pairs

Given the number is 2025, grouping it as 20 and 25.

20 25

Step 2: Consider the first number, which is 20.

Let us find a square number that divides 20

i.e 

1 × 1 = 1 

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

5 × 5 = 25 

The square number that is to be considered for dividing 20 will be 4 x 4

Step 3: Dividing 20 by 4

 Step 4: Continue the division using the next number 20

 The first number to be used as the next divisor is 4 + 4 = 8 (Divisor of first division + quotient of first division) 

Now considering a two digit number starting with 8 to divide 425 will be

81 × 1 = 81

82 × 2 = 164

83 × 3 = 249

84 × 4 = 336

85 × 5 = 425

Continue the division as 

 

Square Root of 2025

Since the Division is complete with remainder as zero, the quotient becomes the square root of the given number. 

Therefore the Square root of 2025 is 45.

Square root of 2025 by Repeated Subtraction Method.

In the repeated subtraction method, 2025 is subtracted repeatedly by odd numbers till zero is obtained. The total number of times the subtraction is performed, becomes the square root. Please note that, if the given number is not a perfect square number, then the result 0 is not obtained.

For the given number 2025, steps for repeated subtraction are

Step 1

2025

1

=

2024

Step 2

2024

3

=

2021

Step 3

2021

5

=

2016

Step 4

2016

7

=

2009

Step 5

2009

9

=

2000

Step 6

2000

11

=

1989

Step 7

1989

13

=

1976

Step 8

1976

15

=

1961

Step 9

1961

17

=

1944

Step 10

1944

19

=

1925

Step 11

1925

21

=

1904

Step 12

1904

23

=

1881

Step 13

1881

25

=

1856

Step 14

1856

27

=

1829

Step 15

1829

29

=

1800

Step 16

1800

31

=

1769

Step 17

1769

33

=

1736

Step 18

1736

35

=

1701

Step 19

1701

37

=

1664

Step 20

1664

39

=

1625

Step 21

1625

41

=

1584

Step 22

1584

43

=

1541

Step 23

1541

45

=

1496

Step 24

1496

47

=

1449

Step 25

1449

49

=

1400

Step 26

1400

51

=

1349

Step 27

1349

53

=

1296

Step 28

1296

55

=

1241

Step 29

1241

57

=

1184

Step 30

1184

59

=

1125

Step 31

1125

61

=

1064

Step 32

1064

63

=

1001

Step 33

1001

65

=

936

Step 34

936

67

=

869

Step 35

869

69

=

800

Step 36

800

71

=

729

Step 37

729

73

=

656

Step 38

656

75

=

581

Step 39

581

77

=

504

Step 40

504

79

=

425

Step 41

425

81

=

344

Step 42

344

83

=

261

Step 43

261

85

=

176

Step 44

176

87

=

89

Step 45

89

89

=

0

Since the result of zero is obtained in the 45th Step, the square root of 2025 is 45.

Video Lessons

Visualising square roots

Finding Square roots

Related Articles

Solved Examples

1. Find the square root of 2025 by pairing factors.

The factors of 2025 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025. The pairs are (1 × 2025), (3 × 675), (5 × 405), (9 × 405), (15 × 225), (25 × 135), (27 × 81), (27 × 75), (45 × 45).  Therefore the square root of 2025 is 45 using pairing factors 45 and 45. 

2. Does zero have a square root?

Zero is the square root of Zero.

Frequently Asked Questions on Square root of 2025

Q1

What is the Square root of 2025?

The Square root of 2025 is 45.
Q2

Give an example where square root is used?

Square and square roots are used in Pythagorean Theorem applications.
Q3

What are the factors of 2025?

The factors of 2025 are 1, 45 and 2025.
Q4

Can a number under square root be split as the sum of square roots?

No. The number under square root cannot be split as the sum of or the difference of square roots .
Q5

2025 is a perfect square number. True or False?

True. 2025 is a perfect square number because square of 45 is 2025.

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*