How to find Square Root of 3364
Square of 58
- 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 58
- To find the square of 58 we multiply 58 by the number itself i.e. by 58 and we write it as follows (58)2 = 58*58= 3364
Square root of 3364
- 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 3364 can be written as,
√3364= √ (58*58) = 58
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 58 and square root of 3364 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 3364 is the positive perfect square which has two roots +58 and -58 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √3364 = √(-58)*(-58) = 58 and √3364 = √(58)*(58) = 58
Similarly,
- (-58)*(-58) = (-58)2 = +3364 and (+58)*(+58) = (+58)2 = 3364
Methods to find square root of perfect square like 3364
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 3364 first we subtract 1 from it.
3364– 1 = 3363
- Then next odd number is 3, so we have to subtract it from 3363
3363– 3 = 3360
- 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 3364 by repeated subtraction method as follows:
3364-1=3363
3363-3=3360
3360-5 = 3355
3355- 7= 3348
3348- 9 =3339
3339-11=3328
3328-13= 3315
3315-15=3300
3300-17=3283
3283-19=3264
3264-21=3243
3243-23=3220
3220-25=3195
3195-27=3168
3168-29=3139
3139-31=3108
3108-33=3075
3075-35=3040
3040-37=3003
3003-39=2964
2964-41=2923
2923-43=2880
2880-45=2835
2835-47=2788
2788-49=2739
26739-51=2688
2688-53=2635
2635-55=2580
2580-57=2523
2523- 59 = 2464
2464- 61 =2403
2403- 63 = 2340
2340- 65 =2275
2275-67=2208
2208-69=2139
2139-71= 2068
2068-73=1995
1995-75=1920
1920-77=1843
1843-79=1764
1,764-81=1683
1683-83=1600
1600-85=1515
1515-87=1428
1428-89=1339
1339-91=1248
1248-93=1115
1115-95=1060
1060-97=963
963-99=864
864-101=763
763-103=660
660-105=555
555-107=448
448-109=339
339-111=228
228-113=115
115-115=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 ,107,109,111,113,115which are 58in numbers.
- Hence, the square root of 3364 by repeated subtraction method is58
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 3364 by prime factorization method.
- As 3364 is even number hence it must be divisible by prime number 2,29
- So, we start from prime number 2 here.
3364÷2=1682
1682÷2=841
841÷29=29
29÷29=1
- Thus, the prime number 2,29used to get remainder as 1 are 2,2,29,29
Thus, 3364=2*2*29*29
And 3364=2*2*29*29
- By taking square root on both sides, we get
√3364=√(2*2*29*29)=√(2*2)√(29*29)=2*29=58
- Thus, we found the square root of 3364 as 58 by using prime factorization method.
Multiple choice questions:
1) Repeated subtraction method is useful for to find out the cube toot.
a) true
b) false
Ans: a) false
2) 3364 is the positive perfect square which has two roots——–
a) +58
b) -58
c) both a and b
d) none of these
Ans: c) both a and b
3) the positive square root value is taken mostly which is called as principal square root
a) true
b) false
Ans: a) true