How to find Square Root of 900
Square of 30:
- 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 30
- To find the square of 30, we multiply 30 by the number itself i.e. by 30 and we write it as follows (30)2 = 30*30 = 900
Square root of 900:
- 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 900 can be written as,
√900 = √ (30*30) = 30
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 30 and square root of 900 as\
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 900 is the positive perfect square which has two roots +30 and -30 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √900 = √(-30)*(-30) = -30 and √900 = √(30)*(30) = 30
Similarly,
- (-30)*(-30) = (-30)2 = +900 and (+30)*(+30) = (+30)2 = 900
Methods to find square root of perfect square like 900:
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 900, first we subtract 1 from it. 900 – 1 = 899
- Then next odd number is 3, so we have to subtract it from 899 899 – 3 = 896
- 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 900 by repeated subtraction method as follows:
900-1=899
899-3=896
896 -5 = 891
891 – 7=884
884 – 9 =875
875-11=864
864 -13= 851
851 -15=836
836-17=819
819-19=800
800-21=779
779-23=756
756-25=731
731-27=704
704-29=675
675-31=644
644 -33=611
611-35=576
576-37=539
539-39=500
500-41=459
459-43=416
416-45=371
371 -47=324
324-49=275
275-51=224
224-53=171
171-55=116
116-57=59
59 – 59 = 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 ,59which are 30 in numbers.
Prime Factorization method:
- Hence, the square root of 900 by repeated subtraction method is 30.
- 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 900 by prime factorization method.
- As 900 is even number hence it must be divisible by prime number 2
- So, we start from prime number 2,5,3here.
900÷ 2 = 450
450÷ 2 = 225
225÷3 = 75
75 ÷3= 25
25÷5 =5
5÷ 5=1
- Thus, the prime number 2,3,5 used to get remainder as 1 are 2,2,3,3,5,5
Thus, 900= 2*2*3*3*5*5
And 900= 2^2*3^2*5^2
- By taking square root on both sides, we get
√900 = √(2*2*3*3*5*5) = 2*3*5 = 30
- Thus, we found the square root of 900 as 30 by using prime factorization method.
Multiple choice questions:
1) the square root of any negative number is always positive
a)true
b) false
Ans: a) true
2) (-30)*(-30)= -900
a) true
b) false
Ans: b) false
3) the prime factor of 900 are——-
a)1,2
b) 2,3,5
c) 7,11
d) all of these
Ans: b) 2,3,5