How to find Square Root of 625
Square of 625:
- 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 25
- To find the square of 25,we multiply 25 by the number itself i.e. by 25 and we write it as follows (625)2 = 25*25= 625
Square root of 625:
- 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 25 can be written as,
√625= √ (25*25) = 25
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 25 and square root of 625 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 625 is the positive perfect square which has two roots +25 and -25 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √625 = √(-25)*(-25) = -25 and √625 = √(25)*(25) = 25
Similarly,
- (-25)*(-25) = (-25)2 = +625 and (+25)*(+25) = (+25)2 = 625
Methods to find square root of perfect square like 625:
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 625, first we subtract 1 from it. 625– 1 =624
- Then next odd number is 3, so we have to subtract it from 624. 624– 3 = 621
- 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 625 by repeated subtraction method as follows:
625−1=624
624−3=621
621−5=616
616−7=609
609−9=600
600−11=589
589−13=576
576−15=561
561−17=544
544−19=525
525−21=504
504−23=481
481−25=456
456−27=429
429−29=400
400−31=369
369−33=336
336−35=301
301−37=264
264−39=225
225−41=184
184−43=141
141−45=96
96−47=49
49−49=0
Thus, here the total odd numbers used are 1, 3, 5, 7, 9, 11, 13, 15 ,17,19,21,23,25,27,29 ,31,33,35 37,39 ,41,43,45,47 and 49which are 25 in numbers.
Hence, the square root of 625 by repeated subtraction method is 25.
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 625 by prime factorization method.
- As 625 is odd number hence it must be divisible by only prime number 5
625÷5=125
125÷5=25
25÷5=5
5÷5=1
- Thus, the prime number25 used to get remainder as 1 are 5,5,5,5
Thus, 625= 5*5*5*5= 5^2*5^2
And 625= (25*25)
- By taking square root on both sides, we get
√625 = √(25*25) = (5*5)
√625 = (5*5)=25
- Thus, we found the square root of 625 as 25 by using prime factorization method.
Multiple choice questions:
1) prime factorization method is used for to find _____
a) prime factor
b) even factor
c) odd factor
d) all of these
Ans: a) prime factor
2) 625 is having square root
a) +25
b) -25
c) Both a and b
d) +15 and -15
And: c) both a and b
3) 25 is the
a) Composite number
b) Odd number
c) Perfect square
d) All of the above
And: d) all of the above