How to find Square Root of 1369
Square of 37:
- 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 37
- To find the square of 37, we multiply 37 by the number itself i.e. by 37 and we write it as follows (37)2 = 37*37 = 1369
Square root of 1369:
- 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 1369 can be written as,
√1369= √ (37*37) = 37
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 37 and square root of 1369 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 1369 is the positive perfect square which has two roots +37 and -37 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √1369 = √(-37)*(-37) = -37 and √1369 = √(37)*(37) = 37
Similarly,
- (-37)*(-37) = (-37)2 = +1369 and (+37)*(+37) = (+37)2 = 1369
Methods to find square root of perfect square like 1369:
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 1369, first we subtract 1 from it.
1369 – 1 = 1368
- Then next odd number is 3, so we have to subtract it from 1368
1368– 3 = 1365
- 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 1369 by repeated subtraction method as follows:
1369-1=1368
1368-3=1365
1365 -5 = 1360
1360 – 7= 1353
1353 – 9 =1344
1344-11=1333
1333 -13= 1320
1320 -15=1305
1305-17=1288
1288-19=1269
1269-21=1248
1248-23=1225
1225-25=1200
1200-27=1173
1173-29=1144
1144-31=1113
1113-33=1080
1080-35=1045
1045-37=1008
1008-39=969
969-41=928
928-43=885
885-45=840
840-47=793
793-49=744
744-51=693
693-53=640
640-55=585
585-57=528
528- 59 = 469
469- 61 =408
408 – 63 = 345
345 – 65 =280
280- 67=213
213-69=144
144-71= 73
73-73=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 which are 37 in numbers.
- Hence, the square root of 1369 by repeated subtraction method is 37
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 1296 by prime factorization method.
- As 1369 is odd number hence it must be divisible by prime number 37
- So, we start from prime number 37 here.
1369÷37= 37
37÷37= 1
- Thus, the prime number 37 used to get remainder as 1 are 37
Thus, 1369= 37*37
And 1369= 37^2
- By taking square root on both sides, we get
√1369 = √(37*37) = 37
- Thus, we found the square root of 1369 as 37 by using prime factorization method.
Multiple choice questions:
1) Square root of 1369 is a natural or a whole number
a) true
b) false
Ans: a) true
2) 1369 is evenly divisible by its square root value, thus, 37 is the factor of 1369.
a) true
b) false
Ans: a) true
3) The roots of 1369 are +37 or -37
a) true
b) false
Ans: a) true