How to find Square Root of 1156
Square of 34:
- 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 34
- To find the square of 34, we multiply 34 by the number itself i.e. by 34 and we write it as follows. (34)2 = 34*34 = 1156
Square root of 1156
- 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 1156can be written as,
√1156= √ (34*34) = 34
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 34 and square root of 1156 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 1156 is the positive perfect square which has two roots +34 and -34 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √1156 = √(-34)*(-34) = -34 and √1156 = √(34)*(34) = 34
Similarly,
- (-34)*(-34) = (-34)2 = +1156 and (+34)*(+34) = (+34)2 = 1156
Methods to find square root of perfect square like 1156:
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 1156, first we subtract 1 from it. 1156 – 1 = 1155
- Then next odd number is 3, so we have to subtract it from 1155. 1155 – 3 = 1152
- 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 1156 by repeated subtraction method as follows:
1156-1=1155
1155-3=1152
1152 -5 = 1147
1147 – 7= 1140
1140 – 9 =1131
1131-11=1120
1120 -13= 1107
1107 -15=1092
1092-17=1075
1075-19=1056
1056-21=1035
1035-23=1012
1012-25=987
987-27=960
960-29=931
931-31=900
900-33=867
867-35=832
832-37=795
795-39=756
756-41=715
715-43=672
672-45=627
627 -47=580
580-49=531
531-51=480
480-53=427
427-55=372
372-57=315
315- 59 = 256
256- 61 =195
195 – 63 = 132
132 – 65 =67
67 – 67=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 61,63,65,67which are 34 in numbers.
- Hence, the square root of 1156 by repeated subtraction method is 34
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 1156 by prime factorization method.
- As 1156 is even number hence it must be divisible by prime number 2
- So, we start from prime number 2 here.
1156÷2= 578
578÷2= 289
289÷17= 17
17÷17=1
- Thus, the prime number 2 and 17used to get remainder as 1 are 2,2,17,17
Thus, 1156= 2*2*17*17
And 1156= 2^2*17^2
- By taking square root on both sides, we get
√1156 = √(2*2*17*17) =√(2*2)√(17*17)=2*17 = 34
- Thus, we found the square root of 1156 as 34 by using prime factorization method.
Multiple choice questions:
1) the square root of 1156 as———-by using prime factorization method
a)11
b)34
c)33
d) none of these
Ans: b) 34
2) 1156 is divisible by smallest prime number—-.
a) 3
b) 5c
c)2
d) 4
Ans: c) 2
3) we can find out the square root of 1156 by repeated subtraction method.
a) true
b) false
Ans: a) true