Square root calculator

In this article I am going to talk about square root calculator. A square root calculator calculates square root of any number of the form x2 = a

For example:  5 is a square root of 25 because 52 = 25

A square is a non negative real number, and square root is any integer other than zero. We can understand this with an example:

√25 = 5 .This is also equal to  52 = 5 x 5 = 25 and here 5 is nonnegative. This root is considered as radicand.

We know every positive number has two square roots, first positive (√a), and another is negative (-√a)

Like above sentence we can say any negative number’s square is always positive. Suppose we have any negative number which is -4 then square root of this number is 16 which is positive. This holds true for all negative numbers’ squares.

√a can be written in exponent notation a1/2 .

In mathematics all numbers are not square roots or perfect squares. We can show this by square root calculator.

So now we see the Square root calculator based examples:

Example: calculate the square root of 10 (√10) correct to one decimal point.

Solution:  for square root problem we will follow the below steps in the square root calculator

Step 1:  First we find the two perfect square numbers which lie around 10.

32 = 9 and 42 = 16, here we can see that √10 is lies between 3 and 4,

Step 2: Now we divide 10 by 3 

10/3 = 3.3 (you can round off your getting value)

Step 3: In this step we find the average of divide value and round off value

Now average = (3.3 + 3)/2 = 3.15

Then we again divide 10 by getting value: 10 / 3.15 = 3.17

Now we again average of getting value 3.17 and previous average value 3.15

Average = (3.15 +3.17)/2 = 3.16

Now we check the square of 3.16 = 9.99 that is not accurate value so we check for 2 decimal places.

In this way we can say that square root 10 in one decimal .We can’t get the accurate value. So we solve this value in two decimal numbers

 

Step 4: in this step we repeat the step 2 means we divide 10 by 3

10/3 = 3.33 (round off the getting value)

Step 5: in this step we repeat the step 3 and find the average for round of value and another two decimal point value

  Average = (3.33 + 3)/2 = 3.165

Now we again divide 10 by average value 3.165 = 10 /3.165 = 3.159

Step 6: in this step we again find the average between above getting value and above average value

 Average = (3.165 +3.159)/2 = 3.162

In this average we can see that square of 3.162 is equal to 9.998 which is equivalent to 10.000

Now we have got the accurate value of 10.

So that was the square root calculator with all steps.

 

 

 

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