Calculating Square Root

Calculating Square root is the basic operation in maths.  We are used calculating square root operation in every day life mathematics.  We are used the symbol for square root is √ . The square root of x will be used in math like `sqrt(x)` . It is also called as radical.

         Square root is a number where the value of a number is multiplied by itself we get the original number.

For example the square root of 25  =   5 squared is 25 that is `5*5`     = 25

So the square root of 25 is 5.  Some of examples of calculating square root,

`sqrt(2)` = 1.414

`sqrt(3)` = 1.732

`sqrt(4)` = 2

`sqrt(5)` = 2.236 etc.

 

Rules for Calculating square root

 

Before we are calculating square root , we need to know some rules of square root operations.

Addition:    `sqrt(m)` + `sqrt(n)` = `sqrt(m+n)`

Subtraction: `sqrt(m)` - `sqrt(n)` = `sqrt(m - n)`

Multiplication:  √m * √n     = √ m * n   

Division:  `sqrt(m)/sqrt(n)`    = `sqrt(m/n)`

 

Looking out for more help on How to Find the Square Root of a Number in Number Sense by visiting listed websites.

 

Calculating square root problems

 

 

Problem 1:

What is the result of square root of 100 divided by square root of 200.

Solution:

Square root of 100 is  `sqrt(100)`

Square root of 200 is `sqrt(200)`

So the division is, `sqrt(100)/sqrt(200)`  = `sqrt(100/200)`

Calculating square root values.

                                       =  `sqrt(1/2)`    = `sqrt(0.5)`   =    0.707

Problem 2:

What is the result of square root values: 6 `sqrt(20)` × `sqrt(45)` × `sqrt(6)`

Solution:

Square root of 6   = `sqrt(6)`  = `sqrt(3*2)`   =` sqrt(3)*sqrt(2)`

Square root of 20 = `sqrt(20)` = `sqrt(5*4)`   =  `sqrt(5)*sqrt(4)` = 2 `sqrt(5)`

Square root of 45 = `sqrt(45)` = `sqrt(9*5)` = `sqrt(9)*sqrt(5)` = 3 `sqrt(5)`

Now we rewrite the expression,

          6 x 2 `sqrt(5)` x 3 `sqrt(5)` x` sqrt (6) `

Now group constant values other than square root,

          ( 6 x 2 x 3 ) `sqrt(5)` `sqrt(5)` `sqrt(6)`

             ( 36 x 5 ) `sqrt(6)`   ( `sqrt(5*5)` = 5 )

                  180 `sqrt(6)`

Calculating square root values

                    180 x 2.45

                          441

 

 

Problem 3:

Calculate the square root values  `sqrt(54756)`

Solution:

For calculating this type of square root values, we will split the number and divide each number for getting the quotient.

Here the quotient value is the square root of a number.

First we take divisor less than value of that square root. 

We split the numbers `sqrt(54756)`   =  5  47  56

                           2    )  5 47 56  (  2 3 4

                                     4            

                            43     1 47                   43 * 3  =  129 

                                     129         

                        464          1 8 5 6           464 * 4 = 1856 

                                        1 8 5 6

                                                 0     

The square root of 54756 `sqrt(54756)` = 234.