How to find Square Root of 3721
Square of 61
- 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 61
- To find the square of 61 we multiply 61 by the number itself i.e. by 61 and we write it as follows (61)2 = 61*61= 3721
Square root of 3721
- 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 3721 can be written as,
√3721= √ (61*61) = 61
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 61 and square root of 3721 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 3721 is the positive perfect square which has two roots +61 and -61 also.
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √3721 = √(-61)*(-61) = 61 and √3721 = √(61)*(61) = 61
Similarly,
- (-61)*(-61) = (-61)2 = +3721 and (+61)*(+61) = (+61)2 = 3721
Methods to find square root of perfect square like 3721
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 3721 first we subtract 1 from it.
3721– 1 = 3720
- Then next odd number is 3, so we have to subtract it from 3720
3720– 3 = 3717
- 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 3721 by repeated subtraction method as follows:
3721-1=3720
3720-3 = 3717
3717-5=3712
3712- 7= 3705
3705- 9 =3696
3696-11=3685
3685-13= 3672
3672-15=3657
3657-17=3640
3650-19=3621
3621-21=3600
3600-23=3577
3577-25=3552
3552-27=3525
3525-29=3496
3496-31=3465
3565-33=3432
3432-35=3397
3397-37=3360
3360-39=3321
3321-41=3280
3280-43=3237
3237-45=3192
3192-47=3145
3145-49=3096
3096-51=3045
3045-53=2992
2992-55=2937
2937-57=2880
2880- 59 = 2821
2821- 61 =2760
2760- 63 = 2697
2697- 65 =2632
2632-67=2565
2565-69=2375
2375-71= 2475
2475-73=2352
2352-75=2277
2277-77=2200
2200-79=2121
2121-81=2040
2040-83=1957
1957-85=1872
1872–87=1785
1785-89=1696
1696-91=1605
1605-93=1512
1512-95=1417
1417-97=1320
1320-99=1221
1221-101=1120
1120-103=1017
1017-105=912
912-107=805
806-109=696
696-111=585
585-113=472
472-115=357
357-117=240
240-119=121
121-121=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 ,87,89,91,93,95 97,99,101,103,105 ,107,109,111,113,115,117,119,121which are 61 in numbers.
- Hence, the square root of 3721 by repeated subtraction method is 61
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 3481 by prime factorization method.
- As 3721 is odd number hence it must be divisible by prime number 61
- So, we start from prime number 61 here.
3721÷61=61
61÷61=1
- Thus, the prime number 61used to get remainder as 1 are 61,61
Thus, 3721=61*61
And 3721=61*61
- By taking square root on both sides, we get
√3721=√(61*61)=61
- Thus, we found the square root of 3721 as 61 by using prime factorization method.
Multiple choice questions:
1) 3721 is odd number hence it must be divisible by prime number
a) 61
b) 67
c)71
d) none of these
Ans: a) 61
2) the positive square root value is taken mostly which is called as non-negative square root.
a) true
b) false
Ans: a) true
3) (+61)*(+61) = (+61)^2 = 3721
a) true
b) false
Ans: a) true