How to calculate square root of a number?

Concept

The square root of a number, let’s say “x,” is denoted by the symbol √ x. It is the value that, when squared (multiplied by itself), equals x. In other words, if y = √ x, then y * y = x.

To calculate the square root using long division, follow these steps:

→Start by grouping the digits of the number into pairs, starting from the decimal point if there is one. If there’s an odd number of digits, the leftmost group will have only one digit. For example, let’s consider the number 6084.

Grouped digits: 60 | 84

→Find the largest perfect square that is less than or equal to the leftmost group. In our example, the largest perfect square less than or equal to 7 , 7*7= 49

→Write the square root of the perfect square as the first digit in the quotient. In our case, the first digit is 7. Now, subtract the product of the digit in the quotient and the perfect square from the leftmost group. Write down the result below the line.

Calculation: 60 – 49 = 11

→Bring down the next group of digits next to the remainder. In our example, we bring down 84 .

New number: 1184

→Double the digit in the quotient and guess the next digit to find a partial quotient. Place this partial quotient above the line, and multiply it by the new number. Write the result below the new number.

Find the largest digit to fill in the units place of the new number, such that when the partial quotient is multiplied by the new number, the result is less than or equal to the current remainder.
7+ 7 = 14 _

→Guess: Let’s guess the next digit as either 2 or 8. Because only these two numbers from 0-9 will give us 4 at one’s place ( no. being 1184 ) 2*2= 4 or 8*8=64
Calculation: 142*2 =284 or 148*8= 1184

After we’ve found the digit to filled , we will have to multiply above and add below like we did previously.

Here we multiply above and add below 148*8 =1184 and then add i.e. 148+8 = 156.

Subtract the product of the digit in the quotient and the number. Write down the result below the line

Here it is 1184-1184= 0

So we stop here.
Since we have reached the end of the grouped digits, our final result is 78.

Therefore, the square root of 6084 is 78 using the long division method.

Calculating square root using calculator=

To calculate the square root using a calculator, first, locate the square root symbol (√) on your calculator. Then, input the number you want to find the square root of and press the square root button (√). The calculator will display the square root of the entered number as the result.

So that’s all about How to calculate square root of a number?

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