How to find Square Root of 4489
Square of 67
- 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 67
- To find the square of 67 we multiply 67 by the number itself i.e. by 67 and we write it as follows (67)2 = 67*67= 4489
Square root of 4489
- 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 4489 can be written as,
√4489= √ (67*67) = 67
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 67 and square root of 4489 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 4489 is the positive perfect square which has two roots +67 and -67 also
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √4489 = √(-67)*(-67) = 67 and √4489 = √(67)*(67) = 67
Similarly,
- (-67)*(-67) = (-67)2 = +4489 and (+67)*(+67) = (+67)2 = 4489
Methods to find square root of perfect square like 4489
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 4489 first we subtract 1 from it.
4489– 1 = 4488
- Then next odd number is 3, so we have to subtract it from 4485
4488– 3 = 4485
- 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 4489 by repeated subtraction method as follows:
4489-1=4488
4488-3 = 4485
4485-5=4480
4480- 7= 4473
4473- 9 =4464
4464-11=4453
4453-13= 4440
4440-15=4425
4425-17=4408
4408-19=4389
4389-21=4368
4368-23=4345
4345-25=4320
4320-27=4293
4293-29=4264
4264-31=4233
4233-33=4200
4200-35=4165
4165-37=4128
4128-39=4089
4089-41=4048
4048-43=4005
4005-45=3960
3960-47=3913
3913-49=3864
3864-51=3813
3813-53=3760
3760-55=3705
3705-57=3648
3648- 59 = 3589
3589- 61 =3528
3528- 63 = 3465
3465- 65 =3400
3400-67=3333
3333-69=3264
3264-71= 3193
3193-73=3120
3120-75=3045
3045-77=2968
2968-79=2889
2889-81=2808
2808-83=2725
2725-85=2660
2660–87=2553
2553-89=2464
2464-91=2373
2373-93=2280
2280-95=2185
2185-97=2088
2088-99=1989
11989-101=1888
188-103=1785
1785-105=1680
1680-107=1573
1573-109=1464
1464-111=1353
1353-113=1240
1240-115=1125
1125-117=1008
1008-119=889
889-121=768
768-123=645
645-125=520
520-127=393
393-129=264
264-131=133
133-133=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 ,107,109,111,113,115,117,119,121,123 ,125,127,129,131,133which are 67 in numbers.
- Hence, the square root of 4489by repeated subtraction method is 67
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 4489 by prime factorization method.
- As 4489 is odd number hence it must be divisible by prime number 67
- So, we start from prime number 67 here.
4489÷67=67
67÷67=1
- Thus, the prime number 67used to get remainder as 1 are 67,67
Thus, 4489=67*67
And 4489=67*67
- By taking square root on both sides, we get
√4489=√(67*67)=67
- Thus, we found the square root of 4489 as 67 by using prime factorization method.
Multiple choice questions:
1) 67 is the prime factor of 4489
a) true
b)false
Ans: a) true
2) the prime factorization of 4489 is 67*67.
a) true
b) false
Ans: a) true
3) 4489 is obtained by ———– 67 consecutive odd numbers
a) subtracting
b) adding
c) multiplying
d) dividing
Ans: a) adding