How to find Square Root of 2401
Square of 49:
- 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 49
- To find the square of 49 we multiply 49 by the number itself i.e. by 49 and we write it as follows (49)2 = 49*49 = 2401
Square root of 2401:
- 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 2401 can be written as,
√2401= √ (49*49) = 49
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 49 and square root of 2401 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 2401 is the positive perfect square which has two roots +49 and -49 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √2401 = √(-49)*(-49) = -49 and √2401 = √(49)*(49) = 49
Similarly,
- (-49)*(-49) = (-49)2 = +2401 and (+49)*(+49) = (+49)2 = 2401
Methods to find square root of perfect square like 2401:
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 2401 first we subtract 1 from it.
2401– 1 = 2400
- Then next odd number is 3, so we have to subtract it from 2400
2400– 3 = 2397
- 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 2401 by repeated subtraction method as follows:
2401-1=2400
2400-3=2397
2397-5 = 2392
2392- 7= 2385
2385- 9 =2376
2376-11=2365
2365-13= 2352
2352-15=2337
2337-17=2320
2320-19=2301
2301-21=2280
2280-23=2257
2258-25=2232
2232-27=2205
2205-29=2176
2176-31=2145
2145-33=2112
2112-35=2077
2077-37=2040
2040-39=2001
2001-41=1960
1960-43=1917
1917-45=1872
1872-47=1825
1825-49=1776
1776-51=1725
1725-53=1672
1672-55=1617
1617-57=1560
1560- 59 = 1501
1501- 61 =1440
1440- 63 = 1377
1377- 65 =1312
1312- 67=1245
1245-69=1176
1176-71= 1105
1105-73=1032
1032-75=957
957-77=880
880-79=801
801-81=720
720-83=637
637-85=552
552-87=465
465-89=376
376-91=285
295-93=192
192-95=97
97-97=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 97which are 49 in numbers.
- Hence, the square root of 2401 by repeated subtraction method is49
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 2401 by prime factorization method.
- As 2401 is odd number hence it must be divisible by prime number 7
- So, we start from prime number 7 here.
2401÷7=343
343÷7=49
49÷7= 7
7÷7=1
- Thus, the prime number 7 used to get remainder as 1 are 7,7,7,7
Thus, 2401= 7*7*7*7
And 2401= 7*7*7*7
- By taking square root on both sides, we get
√2401= √(7*7*7*7)=√(7*7)√(7*7)= 7*7=49
- Thus, we found the square root of 2401 as 49 by using prime factorization method.
Multiple choice questions:
1)square root of 2401 is +49 and -49
a) true
b) false
Ans: a) true
2) square of 49 is 2401
a) true
b) false
Ans: a) true
3) the prime factor of 2401 is 7
a) true
b) false
Ans: a) true