How to find Square Root of 324
Square of 324 :
- 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 18
- To find the square of 18,we multiply 18 by the number itself i.e. by 18 and we write it as follows (324)2 = 18*18= 324
Square root of 324:
- 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 18 can be written as,
√324 = √ (18*18) = 18
Where √ is the symbol which is called as radical sign.
- In short, we remember square of 18 and square root of 324 as
Note:
- Every positive real number has two roots.
- The square of any negative number is always the positive number.
For example:
- 324 is the positive perfect square which has two roots +18 and -18 also.
- But, the positive square root value is taken mostly which is called as principal square root or non-negative square root.
- Hence, √324 = √(-18)*(-18) = -18 and √324 = √(18)*(18) = 18
Similarly,
- (-18)*(-18) = (-18)2 = +324 and (+18)*(+18) = (+18)2 = 324
Methods to find square root of perfect square like 324:
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 324, first we subtract 1 from it.
324 – 1 =323
- Then next odd number is 3, so we have to subtract it from 323
323– 3 = 320.
- 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 324 by repeated subtraction method as follows:
324– 1 = 323
323– 3 = 320
320– 5 = 315
315– 7 = 308
308– 9 = 299
299– 11 = 288
288 – 13 = 275
275– 15 = 260
260 – 17 =243
243 – 19 =224
224 – 21 = 203
203 – 23 = 180
180 – 25 = 155
155 – 27 = 128
128 – 29. = 99
99 – 31 = 68
68 – 33 = 35
35 – 35 = 0
- Thus, here the total odd numbers used are 1, 3, 5, 7, 9, 11, 13, 15 ,17,19,21,23,25,27,29 ,31,33and 35which are 17 in numbers.
- Hence, the square root of 324 by repeated subtraction method is 18.
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 324 by prime factorization method.
- As 324 is even number hence it must be divisible by only two be prime number 18.
324 ÷ 18= 18
18 ÷ 18 = 1
- Thus, the prime number 18 used to get remainder as 1 are 18
Thus, 324= 18*18= 18^2
And 324= (18*18)
- By taking square root on both sides, we get
√324 = √(18*18) = √(18*18)
√324 = (18*18)= 18
- Thus, we found the square root of 324 as 18 by using prime factorization method.
Multiple choice questions:
1) the common factors of 18 and 17 is
a) 1
b) 5
c) 7
d) 18
Ans: a) 1
2) the root value of 324 is
a) +18
b) -18
c) both a and b
d) +324
Ans: c) both a and b
3) The number that can be divide exactly only by itself and 1 are called ———–
a) Integers
b) Prime numbers
c) Whole number
d) Even number
Ans: b) prime number