How to find Square Root of 1089
Square of 33:
- 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 33
- To find the square of 33, we multiply 33 by the number itself i.e. by 33 and we write it as follows. (33)2 = 33*33 = 1089
Square root of 1089:
- 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 1089can be written as,
√1089= √ (33*33) = 33
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 33 and square root of 1089 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 1089 is the positive perfect square which has two roots +33 and -33 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √1089 = √(-33)*(-33) = -33 and √1089 = √(33)*(33) = 33
Similarly,
- (-33)*(-33) = (-33)2 = +1089 and (+33)*(+33) = (+33)2 = 1089
Methods to find square root of perfect square like 1089:
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 1089, first we subtract 1 from it. 1089 – 1 = 1088
- Then next odd number is 3, so we have to subtract it from 1088 1088 – 3 = 1085
- 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 1089 by repeated subtraction method as follows:
1089-1=1088
1088-3=1085
1085 -5 = 1080
1080 – 7= 1073
1073 – 9 =1064
1064-11=1053
1053 -13= 1040
1040-15=1025
1025-17=1008
100819=989
989-21=968
968-23=945
945-25=920
920-27=893
893-29=864
864-31=833
833-33=800
800-35=765
765-37=728
728-39=689
689-41=648
648-43=605
605-45=560
560-47=513
513-49=464
464-51=413
413-53=360
360-55=305
305-57=248
248- 59 = 189
189- 61 =128
128 – 63 = 65
65-65=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, 63,65which are 33 in numbers.
- Hence, the square root of 1089 by repeated subtraction method is 33.
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 1089 by by prime factorization method.
- As 1089 is odd number hence it must be divisible by prime number 3
- So, we start from prime number 3here.
1089÷ 3= 363
363÷ 3= 121
121÷11= 11
11÷11= 1
- Thus, the prime number 3,11used to get remainder as 1 are 3,3,11,11
Thus, 1089= 3*3*11*11
And 1089= 3^2*11^2
- By taking square root on both sides, we get
√1089 = √(3*3*11*11) =√(3*3)√(11*11)=3*11 = 33
- Thus, we found the square root of 1089;as 33 by using prime factorization method.
Multiple choice questions:
1)the square root of 1089 by repeated subtraction method is ——
a) +33
b) 35
c)-33
d) both a and c
Ans: d) both a and c
2) in repeated subtraction method we have to subtract ———
a) successive odd
b) prime number
c)None of these
d) all of these
Ans: a) successive odd
3) √1089=√3*3√11*11=35
a)True
b) false
Ans: b) false