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.
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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.
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