Square Root of 20.2
2026-02-28 17:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-20.2

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from the decimal point. In the case of 20.2, consider it as 20.20 and group it as 20 and 20.

Step 2: Now we need to find n whose square is less than or equal to 20. We can say n is ‘4’ because 4 x 4 = 16, which is less than or equal to 20. Now the quotient is 4; after subtracting 16 from 20, the remainder is 4.

Step 3: Bring down 20, making the new dividend 420. Add the old divisor (4) with itself, giving us 8, which will be our new divisor prefix.

Step 4: Find a digit (x) such that 8x multiplied by x is less than or equal to 420. The number 84 fits because 84 x 4 = 336.

Step 5: Subtract 336 from 420, resulting in a remainder of 84. The quotient so far is 4.4.

Step 6: Add a decimal point and two zeros to the remainder to continue. Now the new dividend is 8400.

Step 7: Repeat the process to find the next digit of the quotient, which will be 9 since 849 x 9 = 7641.

Step 8: Subtract 7641 from 8400, giving a remainder of 759.

Step 9: Continuing this process will yield a more precise square root.

The square root of √20.2 is approximately 4.494.