 # 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 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 ## 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

### What is the Square root of 2025?

The Square root of 2025 is 45.

### Give an example where square root is used?

Square and square roots are used in Pythagorean Theorem applications.

### What are the factors of 2025?

The factors of 2025 are 1, 45 and 2025.

### 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 .

### 2025 is a perfect square number. True or False?

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