How to find Square Root of 2025
Square of 45:
- In mathematics, finding of square of any number is mostly easy because when we multiply the same number with itself then we will get the square of that number.
For example:
- Let us suppose we have to find the square of any number say X, then we multiply X by itself i.e. X and we will get its square as Y. It can be written as (X)2 = X*X= Y
- In similar way we find the square of 45
- To find the square of 45 we multiply 45 by the number itself i.e. by 45 and we write it as follows (45)2 = 45*45 = 2025
Square root of 2025:
- Now, in reverse manner if we have to find the square root of Y. The square root of Y is that single value which when multiplied with itself gives the value Y.
- That means, √Y = √(X*X) = X
Where √ is the symbol named as radical.
For example:
- The square root of 2025 can be written as,
√2025= √ (45*45) = 45
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 45 and square root of 2025 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2025 is the positive perfect square which has two roots +45 and -45 also.
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2025 = √(-45)*(-45) = -45 and √2025 = √(45)*(45) = 45
Similarly,
- (-45)*(-45) = (-45)2 = +2025 and (+45)*(+45) = (+45)2 = 2025
Methods to find square root of perfect square like 2025:
There are many methods to find the square root of perfect squares out of which we see the following method in detail.
- Repeated Subtraction Method
- Prime factorization method
Repeated Subtraction Method:
- In repeated subtraction method, we have to subtract the consecutive odd numbers starting from 1, from the perfect square number whose square root we have to find.
- e. to find square root of 2025 first we subtract 1 from it.
2025– 1 = 2024
- Then next odd number is 3, so we have to subtract it from 2024
2024– 3 = 2021
- In this way, we subtract the consecutive odd numbers from the corresponding values obtained after subtraction continuously till we get final value as 0.
- And the value of number of odd numbers required to get 0 is the required square root.
For example:
- We find the square root of 2025 by repeated subtraction method as follows:
2025-1=2024
2024-3=2021
2021-5 = 2016
2016- 7= 2009
2009- 9 =2000
2000-11=1989
1989 -13= 1976
1976-15=1961
1961-17=1944
1944-19=1925
1925-21=1904
1904-23=1881
1881-25=1856
1856-27=1829
1829-29=1800
1800-31=1769
1769-33=1736
1736-35=1701
1701-37=1664
1664-39=1625
1625-41=1584
1584-43=1541
1541-45=1496
1496-47=1449
1449-49=1400
1400-51=1349
1349-53=1296
1296-55=1241
1241-57=1184
1184- 59 = 1125
1125- 61 =1064
1064- 63 = 1001
1001- 65 =936
936- 67=869
869-69=800
800-71= 729
729-73=656
656-75=581
581-77=504
504-79=425
425-81=344
344-83=261
261-85=176
176-87=89
89-89=0
- Thus, here the total odd numbers used are 1, 3, 5, 7, 9, 12, 13, 15, 17, 19, 21, 23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55 ,57 ,59 61,63,65,67,69 ,71,73,75,77,79,81 ,83,85 ,87,89which are 45 in numbers.
- Hence, the square root of 2025 by repeated subtraction method is45
Prime Factorization method:
- In prime factorization method, we have to divide the perfect square number whose square root we have to find by prime number starting from 2, 3, 5… and so on till we get the remainder as 1.
- Initially we have to divide by prime number 2, if that number is not divisible by 2 then we have to take next prime number i.e. 3 and the process will be continued till we get remainder as 1.
- Finally, we have to make pairs of the prime numbers taken in the form of multiplication and then we have to take its square root.
For example:
- Following is the process to find the square root of 2025by prime factorization method.
- As 2025 is odd number hence it must be divisible by prime number 5
- So, we start from prime number 5 here.
2025÷5=405
405÷5=81
81÷3=27
27÷3=9
9÷3=3
3÷3=1
- Thus, the prime number 45 used to get remainder as 1 are 5,5,3,3,3,3
Thus, 2025= 5*5*3*3*3*3
And 2025= 5*5*3*3*3*3
- By taking square root on both sides, we get
√2025 = √(5*5*3*3*3*3)=√(5*5)√(3*3)√(3*3)=5*3*3=45
- Thus, we found the square root of 2025 as 45 by using prime factorization method.
Multiple choice questions:
1) 2025 is odd number type.
a) true
b) false
Ans: a) true
2) the prime factor of 2025 is 5 and 3
a) true
b) false
Ans: a) true
3) 45 is the square root of 2025
a) true
b) false
Ans: a) true