Square Root Of Seven

SQUARE:

When a particular number is multiplied by itself then the obtained result is known as the square of the original number.

EXAMPLES: (i) Square of 7 = 7 × 7 = 49
(ii) Square of 8 = 8 × 8 = 64

If a number is having its square root as another natural number, the given number is a perfect square.

√4=2

Hence, 4 is a perfect square.

The square root of a number is the number, the square of which is equal to the given number.

It is denoted by the symbol" √ ".

EXAMPLE: √36=6

The square root of seven is indicated by " √7 ".

√7 = 2.64575131106

There are some methods in finding out a square root. The methods are as follows:

However, methods like repeated subtraction along with prime factorization are not applicable if the given number is not a perfect square.

The most commonly used methods to find the square root of any number are the average method and the long division method.

Since 7 is not a perfect square, we will find out its value of square root by using the above-discussed methods.

First of all, look for the perfect square numbers which are within the close range of 7.
So the perfect square numbers near to 7 are 4 and 9, i.e., √4=2 and √9=3.
Therefore, the square root of seven is placed between 2 and 3.
Now, let us divide 7 by 2 or 3.
Dividing 7/3=2.33
Now, find the average for the quotient and divisor, i.e., 2.33+3/2=5.33/2=2.66
Therefore, by using the average method, we get the value of √7=2.66.

The value of the number 7 can also be denoted as 7.000000
We then add a bar from every pair beginning the digit that is highlighted in the “Ones” place. Eg - 7. 00 00 00
Identify the largest value in the square which is less than or equal to the value of the digit present on the extreme left.
(2²<7<3²). So, 2² = 4. Take the number 2 to be the divisor and the number 7 to be the dividend. After completing division we get 3 as the remainder.
We now bring the pair of 00 to the remainder making it 300.
The quotient obtained from the first step is established to be 2. Now we double the quotient which becomes 4 and marks it as the first digit that will be the new divisor.
Identify the largest value which will then fill the gap and will also act as the new digit in the divisor such that the new quotient can be multiplied by the new divisor and the result obtained will be either less or equal to the value of the present dividend 300. 46 x 6 = 276 and is the closest value to 300.
After division we get a new remainder which is 24 and the quotient stands at 2.6.
By continuing the process the final result 2.645 is obtained which is in fact the square root of the number 7.