How to find Square Root of 2916
Square of 54:
- 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 54
- To find the square of 54 we multiply 54 by the number itself i.e. by 54 and we write it as follows (54)2 = 54*54= 2916
Square root of 2916
- 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 2916 can be written as,
√2916= √ (54*54) = 54
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 54and square root of 2916 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2916 is the positive perfect square which has two roots +54 and -54also.
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2916 = √(-54)*(-54) = 53and √2916= √(54)*(54) = 54
Similarly,
- (-54)*(-54) = (-54)2 = +2916 and (+54)*(+54) = (+54)2 = 2916
Methods to find square root of perfect square like 2916:
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 2916 first we subtract 1 from it.
2916– 1 = 2915
- Then next odd number is 3, so we have to subtract it from 2915
2915– 3 = 2912
- 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 2916by repeated subtraction method as follows:
2916-1=2915
2915-3=2912
2912-5 = 2907
2907- 7= 2900
2900- 9 =2891
2891-11=2880
2880-13= 2867
2867-15=2852
2852-17=2835
2835-19=2816
2816-21=2795
2795-23=2772
2772-25=2747
2747-27=2720
2720-29=2691
2691-31=2660
2660-33=2627
2627-35=2592
2592-37=2555
2555–39=2516
2516-41=2475
2475-43=2432
2432-45=2387
2387-47=2340
2340–49=2291
2291-51=2240
2240-53=2187
2187-55=2132
2132-57=2075
2075- 59 = 2016
2016- 61 =1955
1955- 63 = 1892
1892- 65 =1837
1827-67=1760
1760-69=1691
1691-71= 1620
1620-73=1547
1547-75=1472
1472-77=1395
1395-79=1316
1316-81=1235
1235-83=1152
1152-85=1077
1067-87=980
980-89=891
891-91=800
800-93=707
707-95=612
612-97=515
515-99=416
416-101=315
315-103=212
212-105=107
107-107=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 97,99,101,103,105 ,107which are 54 in numbers.
- Hence, the square root of 2916 by repeated subtraction method is54
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 2916 by prime factorization method.
- As 2916 is even number hence it must be divisible by prime number 2,3
- So, we start from prime number 2 here.
2916÷2=1458
1458÷2=729
729÷3=243
243÷3=81
81÷3=27
27÷3=9
9÷3=3
3÷3=1
- Thus, the prime number 2,3 used to get remainder as 1 are 2,2,3,3,3,3,3,3
Thus, 2916=2*2*3*3*3*3*3*3
And 2916=2*2*3*3*3*3*3*3
- By taking square root on both sides, we get
√2916= √(2*2*3*3*3*3*3*3)=√(2*2)√(3*3)√(3*3)√(3*3)=2*3*3*3
- Thus, we found the square root of 2916as 54by using prime factorization method.
Multiple choice questions:
1) 2916 is not divisible by prime number 3
a) true
b) false
Ans: b) false
2) 54 is not prime number
a) true
b) false
Ans: a) true
3) the sum of prime factor of 2916 is 5
a) true
b) false
Ans: a) true