How to find Square Root of 2601
Square of 51:
- 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 51
- To find the square of 51 we multiply 51 by the number itself i.e. by 51 and we write it as follows (51)2 = 51*51 = 2601
Square root of 2601:
- 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 2601 can be written as,
√2601= √ (51*51) = 51
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 51 and square root of 2601 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2601 is the positive perfect square which has two roots +51 and -51 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2601 = √(-51)*(-51) = -51 and √2601= √(51)*(51) = 51
Similarly,
- (-51)*(-51) = (-51)2 = +2601 and (+51)*(+51) = (+51)2 = 2601
Methods to find square root of perfect square like 2601:
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 2601 first we subtract 1 from it.
2601– 1 = 2600
- Then next odd number is 3, so we have to subtract it from 2600
2600– 3 = 2597
- 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 2601 by repeated subtraction method as follows:
2601-1=2600
2600-3=2597
2597-5 = 2592
2592- 7= 2585
2585- 9 =2576
2576-11=2565
2565-13= 2552
2552-15=2537
2537-17=2520
2520-19=2501
2501-21=2480
2480-23=2457
2457-25=2432
2432-27=2405
2405-29=2376
2376-31=2345
2345-33=2312
2311-35=2277
2277-37=2240
2240-39=2201
2201-41=2160
2160-43=2117
2117-45=2072
2072-47=2025
2025-49=1976
1986-51=1925
1925-53=1972
1872-55=1817
1817-57=1760
1760- 59 = 1701
1701- 61 =1640
1640- 63 = 1577
1577- 65 =1512
1512- 67=1445
1445-69=1376
1376-71= 1305
1305-73=1232
1232-75=1157
1157-77=1080
1080-79=1001
1001-81=920
920-83=837
837-85=752
752-87=665
665-89=576
576-91=485
485-93=392
392-95=297
297-97=200
200-99=101
101-101=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 which are 51 in numbers.
- Hence, the square root of 2601 by repeated subtraction method is51
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 2601 by prime factorization method.
- As 2601 is odd number hence it must be divisible by prime number 3,17
- So, we start from prime number 3 here.
2601÷3=867
867÷3=289
289÷17=17
17÷17=1
- Thus, the prime number 3 and 17 used to get remainder as 1 are 3,3,17,17
Thus, 2601=3*3*17*17
And 2601= 3*3*17*17
- By taking square root on both sides, we get
√2601= √(3*3*17*17)=√(3*3)√(17*17)= 3*17=51
- Thus, we found the square root of 2601 as 51 by using prime factorization method.
Multiple choice questions:
1) 2601 is odd number .
a) true
b) false
Ans: a) true
2) Every positive real number has two roots.
a) true
b) false
Ans: a) true
3)The square of any negative number is always the positive number.
a) true
b) false
Ans: a) true