How to find Square Root of 4900
Square of 70
- 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 70
- To find the square of 70 we multiply70 by the number itself i.e. by 70 and we write it as follows (70)2 = 70*70= 4900
Square root of 4900
- 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 4900 can be written as,
√4900= √ (70*70) = 70
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 70 and square root of 4900 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 4900 is the positive perfect square which has two roots +70 and -70 also
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √4900 = √(-70)*(-70)=70 and √4900= √(70 )*(70) = 70
Similarly,
- (-70)*(-70) = (-70)2 = +4900 and (+70)*(+70) = (+70)2 = 4900
Methods to find square root of perfect square like 4900
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 4900 first we subtract 1 from it.
4900– 1 = 4899
- Then next odd number is 3, so we have to subtract it from 4889
4889– 3 = 4896
- 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 4900 by repeated subtraction method as follows:
4900-1=4899
4899-3 = 4896
4896-5= 4891
4891-7= 4884
4884- 9 =4875
4875-11=4864
4864-13= 4851
4851-15=4836
4836-17=4819
4819-19=4800
4800-21=4779
4779-23=4756
4756-25=4731
4731-27=4704
4704-29=4675
4675-31=4644
4644-33=4611
4611-35=4576
4576-37=4539
4539-39=4500
4500-41=4459
4459-43=4416
4416-45=4371
4371-47=4324
4324-49=4275
4275-51=4224
4224-53=4171
4171-55=4116
4116-57=4059
4059- 59 = 4000
4000- 61 =3939
3939- 63 = 3876
3876- 65 =3811
3811-67=3744
3744-69=3675
3675-71= 3604
3604-73=3531
3531-75=3456
3456-77=3379
3379-79=3300
3300-81=3219
3219-83=3136
3136-85=3051
3051-87=2964
2964-89=2875
2875-91=2784
2784-93=2691
2691-95=2596
2596-97=2499
2499-99=2400
2400-101=2299
2299-103=2196
2196-105=2091
2091-107=1984
1984-109=1875
1875-111=1764
1764-113=1651
1651-115=1536
1536-117=1419
1419-119=1300
1300-121= 1179
1179-123=1056
1056-125=931
931-127=804
804-129=675
675-131=544
544-133=411
411-135=276
276-137=139
139-139=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 ,125,127,129,131,133,135,137,139 which are 70 in numbers.
- Hence, the square root of 4900 by repeated subtraction method is 70
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 4900 by prime factorization method.
- As 4900 is even number hence it must be divisible by prime number 2,5,7
- So, we start from prime number 2 here.
4900÷2=2450
2450÷2=1225
1225÷5=245
245÷5=49
49÷7=7
7÷7=1
- Thus, the prime number 2,5,7used to get remainder as 1 are 2,2,5,5,7,7
Thus,4900=2*2*5*5*7*7
And 4900=2*2*5*5*7*7
- By taking square root on both sides, we get
√4900=√(2*2)(5*5)(7*7)=√(2*2)√(5*5)√(7*7)=2*5*7=70
- Thus, we found the square root of 4900 as 70 by using prime factorization method.
Multiple choice questions:
1) Positive square root of 4900 is 70
a) true
b) false
Ans: a) true
2) By prime factorization method square root of 4900 is 70
a) true
b) false
Ans:a) true
3)The prime factor of 4900 are 2,5,7
a) true
b) false
Ans: a) true