How to find Square Root of 2500
Square of 50:
- 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 50
- To find the square of 50 we multiply 50by the number itself i.e. by 50 and we write it as follows (50)2 = 50*50 = 2500
Square root of 2500:
- 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 2500 can be written as,
√2500= √ (50*50) = 50
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 50 and square root of 2500 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2500 is the positive perfect square which has two roots +50 and -50 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2500 = √(-50)*(-50) = -50 and √2500= √(50)*(50) = 50
Similarly,
- (-50)*(-50) = (-50)2 = +2500 and (+50)*(+50) = (+50)2 = 2500
Methods to find square root of perfect square like 2500:
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 2500 first we subtract 1 from it.
2500– 1 = 2499
- Then next odd number is 3, so we have to subtract it from 2499
2499– 3 = 2496
- 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 2500 by repeated subtraction method as follows:
2500-1=2499
2499-3=2496
2496-5 = 2491
2491- 7= 2484
2484- 9 =2475
2475-11=2464
2464-13= 2451
2451-15=2436
2436-17=2419
2419-19=2400
2400-21=2379
2379-23=2356
2356-25=2331
2331-27=2304
2304-29=2275
2275-31=2244
2244-33=2211
2211-35=2176
2176-37=2139
2139-39=2100
2100-41=2059
2059-43=2016
2016-45=1971
1971-47=1924
1924-49=1875
1875-51=1824
1824-53=1771
1771-55=1716
1716-57=1659
1659- 59 = 1600
1600- 61 =1539
1539- 63 = 1476
1476- 65 =1411
1411- 67=1344
1344-69=1275
1275-71= 1204
1204-73=1131
1131-75=1056
1056-77=979
979-79=900
900-81=819
819-83=736
736-85=651
651-87=564
564-89=475
475-91=384
384-93=291
291-95=196
196-97=99
99-99=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 97,99which are 50 in numbers.
- Hence, the square root of 2500 by repeated subtraction method is50
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 2500 by prime factorization method.
- As 2500 is even number hence it must be divisible by prime number 2 and5
- So, we start from prime number 2 here.
2500÷2=1250
1250÷2=625
625÷5=125
125÷5=25
25÷5=5
5÷5=1
- Thus, the prime number 2 and 5 used to get remainder as 1 are 2,2,5,5,5,5
Thus, 2500= 2*2*5*5*5*5
And 2500= 2*2*5*5*5*5
- By taking square root on both sides, we get
√2500= √(2*2*5*5*5*5)=√(2*2)√(5*5)(5*5)= 2*5*5=50
- Thus, we found the square root of 2500 as 50 by using prime factorization method.
Multiple choice questions:
1) the square root of 2500 by repeated subtraction method is50
a) true
b) false
Ans: a) true
2)2500= 2*2*5*5*5*5
a) true
b) false
Ans: a) true
3) the square root of 2500 as 50 by using prime factorization method.
a) true
b) false
Ans: a) true