How to find Square Root of 1225
Square of 35:
- 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 35
- To find the square of 35, we multiply 35 by the number itself i.e. by 35 and we write it as follows (35)2 = 35*35 = 1225
Square root of 1225:
- 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 1225 can be written as,
√1225= √ (35*35) = 35
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 35 and square root of 1225 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 1225 is the positive perfect square which has two roots +35 and -35 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √1225 = √(-35)*(-35) = -35 and √1225 = √(35)*(35) = 35
Similarly,
- (-35)*(-35) = (-35)2 = +1225 and (+35)*(+35) = (+35)2 = 1225
Methods to find square root of perfect square like 1225:
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 1225, first we subtract 1 from it. 1225 – 1 = 1224
- Then next odd number is 3, so we have to subtract it from 1224. 1224– 3 = 1221
- 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 1225 by repeated subtraction method as follows:
1225-1=1224
1224-3=1221
1221 -5 = 1216
1216 – 7= 1209
1209 – 9 =1200
1200-11=1189
1189 -13= 1176
1176 -15=1161
1161-17=1144
1144-19=1125
1125-21=1104
1104-23=1081
1081-25=1056
1056-27=1029
1029-29=1000
1000-31=969
969-33=936
936-35=901
901-37=864
864-39=825
825-41=784
784-43=741
741-45=696
696 -47=649
649-49=600
600-51=549
549-53=496
496-55=441
441-57=384
384- 59 = 325
325- 61 =264
264 – 63 = 201
201 – 65 =136
136 – 67=69
69-69=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 which are 35 in numbers.
- Hence, the square root of 1225 by repeated subtraction method is 35
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 1225 by prime factorization method.
- As 1225 is and number hence it must be divisible by prime number 5 and 7
- So, we start from prime number 5 here.
1225÷5= 245
245÷5= 49
49÷7= 7
7÷7=1
- Thus, the prime number 5 and 7used to get remainder as 1 are 5,5,7,7
Thus, 1225= 5*5*7*7
And 1225= 5^2*7^2
- By taking square root on both sides, we get
√1225 = √(5*5*7*7) =√(5*5)√(7*7)= 5*7 = 35
- Thus, we found the square root of 1225 as 35 by using prime factorization method.
Multiple choice questions:
1)The square root of 1225 in radical form is expressed as
a) 1225
b)√1225
c)3√1225
d) none of these
Ans: b) √1225
2) The value of the square of square root of 1225 is ——-
a) 35
b)-35
c)1225
d)+35 and-35
Ans: c) 1225
3) 1225 is a perfect square
a) true
b) false
Ans: a) true