How to find Square Root of 2116
Square of 46:
- 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 46
- To find the square of 46 we multiply 46 by the number itself i.e. by 46 and we write it as follows. (46)2 = 46*46 = 2116
Square root of 2116:
- 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 2116 can be written as,
√2116= √ (46*46) = 46
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 46 and square root of 2116 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2116 is the positive perfect square which has two roots +46 and -46 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2116 = √(-46)*(-46) = -46 and √2116 = √(46)*(46) = 46
Similarly,
- (-46)*(-46) = (-46)2 = +2116 and (+46)*(+46) = (+46)2 = 2116
Methods to find square root of perfect square like 2116:
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 2116 first we subtract 1 from it.
2116– 1 = 2115
- Then next odd number is 3, so we have to subtract it from 2115
2115– 3 = 2112
- 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 2116 by repeated subtraction method as follows:
2116-1=2115
2115-3=2112
2112-5 = 2107
2107- 7= 2100
2100- 9 =2091
2091-11=2080
2080 -13= 2067
2067-15=2052
2052-17=2035
2035-19=2016
2016-21=1995
1995-23=1972
1972-25=1947
1947-27=1920
1920-29=1891
1891-31=1860
1860-33=1827
1827-35=1792
1792-37=1755
1755-39=1716
1716-41=1675
1675-43=1632
1632-45=1587
1587-47=1540
1540-49=1491
1491-51=1440
1440-53=1387
1387-55=1332
1332-57=1275
1275- 59 = 1216
1216- 61 =1155
1155 63 = 1092
1092- 65 =1027
1027- 67=960
960-69=891
891-71= 820
820-73=747
747-75=672
672-77=595
595-79=516
516-81=435
435-83=352
352-85=267
267-87=180
180-89=91
91-91=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 ,87,89,91which are 46 in numbers.
- Hence, the square root of 2116 by repeated subtraction method is46
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 2116by prime factorization method.
- As 2116 is even number hence it must be divisible by prime number 2 and23
- So, we start from prime number 2 here.
2116÷2=1058
1058÷2=529
529÷23=23
23÷23=1
- Thus, the prime number 46 used to get remainder as 1 are 2,2,23,23
Thus, 2116= 2*2*23*23
And 2116= 2*2*23*23
- By taking square root on both sides, we get
√2116 = √(2*2*23*23)=√(2*2)√(23*23)=23*2=46
- Thus, we found the square root of 2116 as 46 by using prime factorization method.
Multiple choice questions:
a) 2116 is not divisible by 23.
a) true
b) false
Ans: b) false
2)the product of prime factor of 2116 is even number
a) true
b) false
Ans: a) true
3) the addition of prime factor of 2116 is odd number
a) true
b) false
Ans: a) true