How to find Square Root of 1849
Square of 43:
- 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 43
- To find the square of 43 we multiply 43 by the number itself i.e. by 43 and we write it as follows (43)2 = 43*43 = 1849
Square root of 1849
- 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 1849 can be written as,
√1849= √ (43*43) = 43
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 43 and square root of 1849 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 1849 is the positive perfect square which has two roots +43 and -43 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √1849= √(-43)*(-43) = -43 and √1849 = √(43)*(43) = 43
Similarly,
- (-43)*(-43) = (-43)2 = +1849 and (+43)*(+43) = (+43)2 = 1849
Methods to find square root of perfect square like 1849:
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 1849 first we subtract 1 from it.
1849– 1 = 1848
- Then next odd number is 3, so we have to subtract it from 1848
1848– 3 = 1845
- 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 1849 by repeated subtraction method as follows:
1849-1=1848
1848-3=1845
1845-5 = 1840
1840- 7= 1833
1833- 9 =1824
1824-11=1813
1813 -13= 1800
1800-15=1785
1785-17=1768
1768-19=1749
1749-21=1728
1728-23=1705
1705-25=1680
1680-27=1653
1653-29=1624
1624-31=1593
1593-33=1560
1560-35=1525
1525-37=1488
1488-39=1449
1449-41=1408
1408-43=1365
1365-45=1320
1320-47=1273
1273-49=1224
1224-51=1173
1173-53=1120
1120-55=1065
1065-57=1008
1008- 59 = 949
949- 61 =888
888- 63 = 825
825- 65 =760
760- 67=693
693-69=624
624-71= 553
553-73=480
480-75=405
405-77=328
328-79=249
249-81=168
168-83=85
85-85=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 ,83,85which are 43 in numbers.
- Hence, the square root of 1849 by repeated subtraction method is43
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 1764 by prime factorization method.
- As 1849 is odd number hence it must be divisible by prime number 43
- So, we start from prime number 43 here.
1849÷43= 43
43÷43= 1
- Thus, the prime number 43 used to get remainder as 1 are 43,43
Thus, 1849= 43*43
And 1849= 243*43
- By taking square root on both sides, we get
√1849 = √(43*43)=43
- Thus, we found the square root of 1849 as 43 by using prime factorization method.
Multiple choice questions:
1) by using repeated subtraction method the square root of 1849 is——
a) 18
b)43
c) 48
d)45
Ans: a) 43
2) 1849 is a prime number.
a) true
b) false
Ans: a) false
3) 43 is a prime number
a) true
b) false
Ans: a) true