How to find Square Root of 2704
Square of 52:
- 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 52
- To find the square of 52 we multiply 52 by the number itself i.e. by 52 and we write it as follows (52)2 = 52*52 = 2704
Square root of 2704:
- 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 2704 can be written as,
√2704= √ (52*52) = 52
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 52 and square root of 2704 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2704 is the positive perfect square which has two roots +52 and -52 also.
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2704 = √(-52)*(-52) = 52 and √2704= √(52)*(52) = 52
Similarly,
- (-52)*(-52) = (-52)2 = +2704 and (+52)*(+52) = (+52)2 = 2704
Methods to find square root of perfect square like 2704:
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 2704 first we subtract 1 from it.
2704– 1 = 2703
- Then next odd number is 3, so we have to subtract it from 2703
2703– 3 = 2700
- 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 2704 by repeated subtraction method as follows:
2704-1=2703
2703-3=2700
2700-5 = 2695
2695- 7= 2688
2688- 9 =2679
2679-11=2668
2668-13= 2655
2655-15=2640
2640-17=2623
2623-19=2604
2604-21=2583
2583-23=2560
2560-25=2535
2535–27=2508
2508-29=2479
2479-31=2448
2448-33=2415
2415-35=2380
2380-37=2343
2343–39=2304
2304-41=2263
2263-43=2220
2220-45=2175
2175-47=2128
2128–49=2079
2079-51=2028
2028-53=1975
1975-55=1920
1920-57=1863
1863- 59 = 1804
1804- 61 =1743
1743- 63 = 1680
1680- 65 =1615
1615- 67=1548
1548-69=1479
1479-71= 1408
1408-73=1335
1335-75=1260
1260-77=1183
1183-79=1104
1104-81=1023
1023-83=940
940-85=855
855-87=768
768-89=679
679-91=588
588-93=495
495-95=400
400-97=303
303-99=204
204-101=103
103-103=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 97,99,101,103 which are 52 in numbers.
- Hence, the square root of 2704 by repeated subtraction method is52
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 2704 by prime factorization method.
- As 2704 is even number hence it must be divisible by prime number 2 and13
- So, we start from prime number 2here.
2704÷2=1352
1352÷2=676
676÷2=338
338÷2=169
169÷13=13
13÷13=1
- Thus, the prime number 2and 13 used to get remainder as 1 are 2,2,2,2,13,13
Thus, 2704=2*2*2*2*13*13
And 2704= 2*2*2*2*13*13
- By taking square root on both sides, we get
√2704= √(2*2*2*2*13*13)=√(2*2)√(13*13)√(2*2)= 2*2*13=52
- Thus, we found the square root of 2704 as 52 by using prime factorization method.
Multiple choice questions:
1) 2704 is the positive perfect square which has two roots +52 and -52 .
a) true
b)false
Ans: a) true
2) 2704 is even number hence it must not be divisible by prime number 2
a) true
b) false
Ans: b) false
3) √2704 = √(-52)*(-52) = -52
a) true
b) false
Ans:b) false