How to find Square Root of 3136
Square of 56
- 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 56
- To find the square of 56 we multiply 56 by the number itself i.e. by 56 and we write it as follows (56)2 = 56*56= 3136
Square root of 3136
- 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 3116 can be written as,
√3136= √ (56*56) = 56
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 56 and square root of 3136 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 3136is the positive perfect square which has two roots +56 and -56also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √3136= √(-56)*(-56) = 56and √3136= √(56)*(56) = 56
Similarly,
- (-56)*(-56) = (-56)2 = +3136 and (+56)*(+56) = (+56)2 = 3136
Methods to find square root of perfect square like 3136
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 3136 first we subtract 1 from it.
3136– 1 = 3135
- Then next odd number is 3, so we have to subtract it from 3135
3135– 3 = 3132
- 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 3136 by repeated subtraction method as follows:
3136-1=3135
3135-3=3132
3132-5 = 3127
3127- 7= 3120
3120- 9 =3111
3111-11=3100
3100-13= 3087
3087-15=3072
3072-17=3055
3055-19=3036
3036-21=3015
3015-23=2992
2992-25=2967
2967-27=2940
2940-29=2911
2911-31=2880
2880-33=2847
2847-35=2812
2812-37=2775
2775-39=2736
2736-41=2695
2695-43=2652
2652-45=2607
2607-47=2560
2560-49=2511
2511-51=2460
2460-53=2407
2407-55=2352
2352-57=2295
2295- 59 = 2236
2236- 61 =2175
2175- 63 = 2112
2112- 65 =2047
2047-67=1980
1980-69=1911
1911-71= 1840
1840-73=1767
1767-75=1692
1692-77=1615
1615-79=1536
1536-81=1455
1455-83=1372
1372-85=1287
1287-87=1200
1200-89=1111
1111-91=1020
1020-93=927
927-95=832
832-97=735
735-99=636
636-101=535
535-103=432
432-105=327
327-107=220
220-109=111
111-111=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 ,107,109,111which are 56in numbers.
- Hence, the square root of 3136 by repeated subtraction method is56
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 3136 by prime factorization method.
- As 3136 is even number hence it must be divisible by prime number 2 and 7
- So, we start from prime number 2 here.
3136÷2=1568
1568÷2=784
784÷2=392
392÷2=196
196÷2=98
98÷2=49
49÷7=7
7÷7=1
- Thus, the prime number 2,7used to get remainder as 1 are 2,2,2,2,2,2,7,7
Thus, 3136=2*2*2*2*2*2*7*7
And 3136=2*2*2*2*2*2*7*7
- By taking square root on both sides, we get
√3136=√(2*2*2*2*2*2*7*7)=√(2*2)√(2*2)√(2*2)√(7*7)=2*2*2*7=56
- Thus, we found the square root of 3136 as 56 by using prime factorization method.
Multiple choice questions:
1) √3136=?
a)2*2*2*7
b) 2*2*2*2*7*7
c) 4*5*6
d) none of these
Ans: a) 2*2*2*7
2) In prime factorization method, we have to divide the perfect square number whose square root we have to find by prime number starting from ——–
a) 1
b)0
c)7
d)2
Ans: d) 2
3) 3136 is even number hence it must be divisible by prime number ———
a) 3,5
b) 11,13
c) 17,19
d) 2,7
Ans: d)2,7