How to find Square Root of 4225

How to find Square Root of 4225

Square of 65

  • 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 65
  • To find the square of 65 we multiply 65 by the number itself i.e. by 65 and we write it as follows (65)2 = 65*65= 4225

Square root of 4225

  • 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 4225 can be written as,

√4225= √ (65*65) = 65

Where is the symbol which is called as radical sign.

  • In short, we remember square of 65 and square root of 4225 as

Note:

  • Every positive real number has two roots.
  • The square of any negative number is always the positive number.

 

For example:

  • 4225 is the positive perfect square which has two roots +65 and -65 also
  • But, the positie square root value is taken mostly which is called as principal square root or non-negative square root.
  • Hence, √4225 = √(-65)*(-65) = 65 and √4225 = √(65)*(65) = 65

 Similarly,

  • (-65)*(-65) = (-65)2 = +4225 and (+65)*(+65) = (+65)2 = 4225

Methods to find square root of perfect square like 4225

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 4225 first we subtract 1 from it.

4225– 1 = 4224

  • Then next odd number is 3, so we have to subtract it from 4224

4224– 3 = 4221

  • 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 4225 by repeated subtraction method as follows:

4225-1=4224

4224-3 = 4221

4221-5=4216

4216- 7= 4209

4209- 9 =4200

4200-11=4189

4189-13= 4176

4176-15=4161

4161-17=4144

4144-19=4125

4125-21=4104

4104-23=4081

4081-25=4056

4056-27=4029

4029-29=4000

4000-31=3969

3969-33=3936

3936-35=3901

3901-37=3864

3864-39=3825

3825-41=3784

3784-43=3741

3741-45=3697

3696-47=3649

3649-49=3600

3600-51=3549

3549-53=3496

3496-55=3441

3441-57=3384

3384- 59 = 3325

3325- 61 =3264

3264-  63 = 3201

3201- 65 =3136

3136-67=3069

3069-69=3000

3000-71= 2929

2929-73=2856

2856-75=2781

2781-77=2704

2704-79=2625

2625-81=2544

2544-83=2461

2461-85=2376

2376–87=2289

2289-89=2200

2200-91=2109

2109-93=2016

2016-95=1921

1921-97=1824

1824-99=1725

1725-101=1624

1624-103=1521

1521-105=1416

1416-107=1309

1309-109=1200

1200-111=1089

1089-113=976

976-115=861

861-117=744

744-119=625

625-121= 504

504-123=381

381-125=256

256-127=129

129-129=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 ,125,127,129which are 65 in numbers.
  • Hence, the square root of 4225by repeated subtraction method is 65

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 4225 by prime factorization method.
  • As 4225 is odd number hence it must be divisible by prime number 5,13
  • So, we start from prime number 5 here.

4225÷5=845

845÷5=169

169÷13=13

13÷13=1

  • Thus, the prime number 5,13used to get remainder as 1 are 5,5,13,13

Thus, 4225=13*13*5*5

And 4225=13*13*5*5

  • By taking square root on both sides, we get

√4225=√(5*5)(13*13)=√(5*5)√(13*13)=5*13=65

  • Thus, we found the square root of 4225 as 65  by using prime factorization method.

 

Multiple Choice Questions:

 

1) Square root of 4225 by repeated subtraction method is ——-

a) 66

b) 65

c) 56

d) 67

Ans: b) 65

 

2) 4225=13*13—-*—-

a)5,5

b)6,6

c)7,7

d)9,9

Ans: a) 5,5

 

3) 4225 is divisible by prime no.——

a) 3

b)2

c)5

d)7

Ans: c)5

Updated: March 29, 2022 — 11:04 am

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