How to find Square Root of 3844
Square of 62
- 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 62
- To find the square of 62 we multiply 62 by the number itself i.e. by 62 and we write it as follows (62)2 = 62*62= 3844
Square root of 3844
- 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 3844 can be written as,
√3844= √ (62*62) = 62
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 62 and square root of 3844 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 3844 is the positive perfect square which has two roots +62 and -62 also.
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √3844 = √(-62)*(-62) = 62 and √3844 = √(62)*(62) = 62
Similarly,
- (-62)*(-62) = (-62)2 = +3844 and (+62)*(+62) = (+62)2 = 3844
Methods to find square root of perfect square like 3844
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 3844 first we subtract 1 from it.
3844– 1 = 3843
- Then next odd number is 3, so we have to subtract it from 3843
3843– 3 = 3840
- 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 3844 by repeated subtraction method as follows:
3844-1=3843
3843-3 = 3840
3840-5=3835
3835- 7= 3828
3828- 9 =3819
3819-11=3808
3808-13= 3795
3795-15=3780
3780-17=3763
3763-19=3744
3744-21=3723
3723-23=3700
3700-25=3675
3675-27=3648
3648-29=3619
3619-31=3588
3588-33=3555
3555-35=3520
3520-37=3483
3483-39=3444
3444-41=3403
3403-43=3360
3360-45=3315
3315-47=3268
3268-49=3219
3219-51=3168
3168-53=3115
3115-55=3060
3060-57=3003
3003- 59 = 2944
2944- 61 =2883
2883- 63 = 2820
2820- 65 =2755
2755-67=2688
2688-69=2619
2619-71= 2548
2548-73=2475
2475-75=2400
2400-77=2323
2323-79=2244
2244-81=2263
2263-83=2080
2080-85=1995
1995–87=1908
1908-89=1819
1819-91=1728
1728-93=1635
1635-95=1540
1540-97=1443
1443-99=1344
1344-101=1243
1243-103=1140
1140-105=1034
1035-107=928
928-109=819
819-111=708
708-113=595
595-115=480
480-117=363
363-119=244
244-121= 123
123-123=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 ,107,109,111,113,115,117,119,121,123which are 62 in numbers.
- Hence, the square root of 3844 by repeated subtraction method is 62
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 3844 by prime factorization method.
- As 3844 is even number hence it must be divisible by prime number 2,31
- So, we start from prime number 2 here.
3844÷2=1922
1922÷2=961
961÷31=31
31÷31=1
- Thus, the prime number used to get remainder as 1 are 2,2,31,31
Thus, 3844=2*2*31*31
And 3844=2*2*31*31
- By taking square root on both sides, we get
√3844=√(2*2)(31*31)=√(2*2)√(31*31)=2*31=62
- Thus, we found the square root of 3844 as 62 by using prime factorization method.
Multiple choice questions:
1) Square root of 3844 is 62.
a) true
b) false
Ans: a) true
2) square of 62 is(- 3844)
a) true
b)false
Ans: b) false
3) In non-negative square root we taken negative square root value mostly
a) true
b) false
Ans: b) false