How to find Square Root of 1521
Square of 39:
- 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 39
- To find the square of 39, we multiply 39 by the number itself i.e. by 39 and we write it as follows (39)2 = 39*39 = 1521
Square root of 1521:
- 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 1521 can be written as,
√1521= √ (39*39) = 39
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 39 and square root of 1521 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 1521 is the positive perfect square which has two roots +39 and -39 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √1521 = √(-39)*(-39) = -39 and √1521 = √(39)*(39) = 39
Similarly,
- (-39)*(-39) = (-39)2 = +1521 and (+39)*(+39) = (+39)2 = 1521
Methods to find square root of perfect square like 1521:
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 1521, first we subtract 1 from it.
1521 – 1 = 1520
- Then next odd number is 3, so we have to subtract it from 1520
1520– 3 = 1517
- 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 1521 by repeated subtraction method as follows:
1521-1=1520
1520-3=1517
1517 -5 = 1512
1512- 7= 1505
1505 – 9 =1496
1496-11=1485
1485 -13= 1472
1472 -15=1457
1457-17=1440
1440-19=1421
1421-21=1400
1400-23=1377
1377-25=1352
1352-27=1325
1325-29=1296
1296-31=1265
1265-33=1232
1232-35=1197
1197-37=1160
1160-39=1121
1121-41=1080
1080-43=1037
1037-45=992
992-47=945
945-49=896
896-51=845
845-53=792
792-55=737
737-57=680
680- 59 = 621
621- 61 =560
560 – 63 = 497
497 – 65 =432
432- 67=365
365-69=296
296-71= 225
225-73=152
152-75=77
77-77=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 which are 39 in numbers.
- Hence, the square root of 1521 by repeated subtraction method is 39
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 1296 by prime factorization method.
- As 1521 is odd number hence it must be divisible by prime number 3 and13
- So, we start from prime number 3 here.
1521÷3= 507
507÷3= 169
169÷13=13
13÷13=1
- Thus, the prime number 3 and13 used to get remainder as 1 are 3,3,13,13
Thus, 1521= 3*3*13*13
And 1521= 3^2*13^2
- By taking square root on both sides, we get
√1521 = √(3*3)(13*13) = √(3*3)√(13*13)=3*13=39
- Thus, we found the square root of 1521 as 39 by using prime factorization method.
Multiple choice questions:
1) the square root of 1521 using the prime factorization method.
a) true
b) false
Ans: a) true
2) The square root of 1521 is a rational number as it can be expressed in the form of p/q.
a) true
b) false
Ans: a) true
3) The square root of 1521 is symbolically expressed as —–+
a)3√1521
b√(1521)^2
c)1521
d)√1521
Ans: d)√1521