How to find Square Root of 3600
Square of 60
- 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 60
- To find the square of 60 we multiply 60 by the number itself i.e. by 60 and we write it as follows (60)2 = 60*60= 3600
Square root of 3600
- 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 3600 can be written as,
√3600= √ (60*60) = 60
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 60 and square root of 3600 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 3600 is the positive perfect square which has two roots +60 and -60 also.
- But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √3600 = √(-60)*(-60) = 60 and √3600 = √(60)*(60) = 60
Similarly,
- (-60)*(-60) = (-60)2 = +3600 and (+60)*(+60) = (+60)2 = 3600
Methods to find square root of perfect square like 3600
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 3600 first we subtract 1 from it.
3600– 1 = 3599
- Then next odd number is 3, so we have to subtract it from 3480
3599– 3 = 3596
- 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 3600 by repeated subtraction method as follows:
3600-1=3599
3599-3 = 3596
3596-5=3591
3591- 7= 3584
3584- 9 =3575
3575-11=3564
3564-13= 3551
3551-15=3536
3536-17=3519
3519-19=3500
3500-21=3479
3479-23=3456
3456-25=3431
3431-27=3404
3405-29=3375
3375-31=3344
3344-33=3317
3317-35=3276
3276-37=3239
3239-39=3200
3200-41=3159
3159-43=3116
3116-45=3071
3071-47=3024
3024-49=2975
2975-51=2924
2924-53=2871
2871-55=2816
2816-57=2759
2759- 59 = 2700
2700- 61 =2639
2639- 63 = 2576
2576- 65 =2511
2511-67=2444
2444-69=2375
2375-71= 2304
2304-73=2231
2231-75=2156
2156-77=2079
2079-79=2000
2000-81=1919
1919-83=1836
1836-85=1751
1751–87=1664
1664-89=1575
1575-91=1484
1484-93=1391
1391-95=1296
1296-97=1199
1199-99=1100
1100-101=999
999-103=897
897-105=791
791-107=684
684-109=575
575-111=464
464-113=351
351-115=236
236-117=119
119-119=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 ,107,109,111,113,115,117,119which are 59 in numbers.
- Hence, the square root of 3600 by repeated subtraction method is 60
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 3481 by prime factorization method.
- As 3600 is even number hence it must be divisible by prime number 2
- So, we start from prime number 60 here.
3600÷2=1800
1800÷2=900
900÷2=450
450÷2=225
225÷5=45
45÷5=9
9÷3=3
3÷3=1
- Thus, the prime number 2,5,3 used to get remainder as 1 are 2,2,2,2,5,5,3,3
Thus, 3600=2*2*2*25*5*3*3
And 3600=2*2*2*2*5*5*3*3
- By taking square root on both sides, we get
√3600=√(2*2*2*2*3*3*5*5)=√(2*2)√(2*2)√(5*5)√(3*3)=2*2*5*3=60
- Thus, we found the square root of 3600 as 60 by using prime factorization method.
Multiple choice questions:
1) the square root of 3600 as 60 by using prime factorization method
a) true
b) false
Ans: a) true
2) the square root of 3600 by repeated subtraction method is 60
a) true
b) false
Ans: a) true
3) Square of 60 is 3600.
a) true
b) false
Ans: a) true