How to find Square Root of 361
Square of 361 :
- 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 19
- To find the square of 19,we multiply 19 by the number itself i.e. by 19 and we write it as follows.
- (361)2 = 19*19= 361
Square root of 361:
- 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 19 can be written as,
√361 = √ (19*19) = 19
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 19 and square root of 361 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 361 is the positive perfect square which has two roots +19 and -19 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √361 = √(-19)*(-19) = -19 and √361 = √(19)*(19) = 19
Similarly,
- (-19)*(-19) = (-19)2 = +361 and (+19)*(+19) = (+19)2 =361
Methods to find square root of perfect square like 361:
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 361, first we subtract 1 from it. 361 – 1 = 360
- Then next odd number is 3, so we have to subtract it from 360. 360– 3 = 357
- 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 361 by repeated subtraction method as follows:
361– 1 = 360
360– 3 = 357
357– 5 = 352
352– 7 = 345
345– 9 = 336
336– 11 = 325
325 – 13 = 312
312– 15 = 297
297 – 17 =280
280 – 19 =261
261 – 21 = 240
240 – 23 = 217
217 – 25 = 192
192 – 27 = 165
165 – 29. = 136
136 – 31 = 105
105 – 33 = 72
72 – 35 = 37
37 – 37 = 0
- Thus, here the total odd numbers used are 1, 3, 5, 7, 9, 11, 13, 15 ,17,19,21,23,25,27,29,31,33,35, and 37which are 19 in numbers.
- Hence, the square root of 361 by repeated subtraction method is 19.
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 81 by prime factorization method.
- As 361 is odd number hence it must be divisible by prime number 19
361 ÷ 19= 19
19 ÷ 19 = 1
- Thus, the prime number 19 used to get remainder as 1 are 19,19
Thus, 361= 19*19= 19^2
And 361= (19*19)
- By taking square root on both sides, we get
√361 = √(19*19)= √(19*19)
√361 = 19
- Thus, we found the square root of 361 as 19 by using prime factorization method.
Multiple choice questions:
1) 361 is a ———-type of number
a) prime
b)composite
c)even
d)all of these
Ans: b) composite
2) 361 is divisible by ———— number.
a) 4
b) 18
c) 19
d) 20
Ans: c) 19
3) prime factorization involve only ———.
a) Composite number
b) Prime number
c) Even number
d) None of these
Ans: b) prime number