How to find Square Root of 3481
Square of 59
- 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 59
- To find the square of 59 we multiply 59 by the number itself i.e. by 59 and we write it as follows (59)2 = 59*59= 3481
Square root of 3481
- 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 3481 can be written as,
√3481= √ (59*59) = 59
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 59 and square root of 3481 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 3481 is the positive perfect square which has two roots +59 and -59 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √3481 = √(-59)*(-59) = 59 and √3481 = √(59)*(59) = 59
Similarly,
- (-59)*(-59) = (-59)2 = +3481 and (+59)*(+59) = (+59)2 = 3481
Methods to find square root of perfect square like 3481
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 3481 first we subtract 1 from it.
3481– 1 = 3480
- Then next odd number is 3, so we have to subtract it from 3480
3480– 3 = 3477
- 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 3481 by repeated subtraction method as follows:
3481-1=3480
3480-3=3477
3477-5 = 3472
3472- 7= 3465
3465- 9 =3456
3456-11=3445
3445-13= 3432
3432-15=3417
3417-17=3400
3400-19=3381
3381-21=3360
3360-23=3337
3337-25=3312
3312-27=3285
3285-29=3256
3256-31=3225
3225-33=3192
3192-35=3157
3157-37=3120
3120-39=3081
3081-41=3040
3040-43=2997
2997-45=2952
2952-47=2905
2905-49=2856
2856-51=2805
2805-53=2752
2752-55=2697
2697-57=2640
2640- 59 = 2581
2581- 61 =2520
2520- 63 = 2457
2457- 65 =2392
2392-67=2325
2325-69=2256
2256-71= 2185
2185-73=2112
2112-75=2037
2037-77=1960
1960-79=1881
1,881-81=1800
1800-83=1717
1717-85=1632
1632–87=1545
1545-89=1456
1456-91=1365
1365-93=1272
1272-95=1177
1177-97=1080
1080-99=981
981-101=880
880-103=777
777-105=672
672-107=565
565-109=456
456-111=345
345-113=233
232-115=117
117-117=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 ,107,109,111,113,115,117which are 59 in numbers.
- Hence, the square root of 3481 by repeated subtraction method is59
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 3481 is odd number hence it must be divisible by prime number 59
- So, we start from prime number 59here.
3481÷59=59
59÷59=1
- Thus, the prime number 59 used to get remainder as 1 are 59,59
Thus, 3481=59*59
And 3481=59*59
- By taking square root on both sides, we get
√3481=√(59*59)=59
- Thus, we found the square root of 3481 as 59 by using prime factorization method.
Multiple choice questions:
1) 59 is not a prime number.
a) true
b) false
Ans: a) true
2) 3481 is a perfect square of 59
a) true
b) False
ans: a) true
3) 3481 is a prime number
a) true
b) false
Ans: b) false