what is square root of 0.31428 from divison method.

It's 0.5606068140863.

or 9√970/500.

To find the square root of 0.31428 using the division method, follow these steps:

Step 1: Start by grouping the digits in the number in pairs from the decimal point. For 0.31428, we have 31 and 428.

Step 2: Find the largest perfect square that is less than or equal to the first group of digits (31 in this case). The largest perfect square less than 31 is 25, which is equal to 5^2.

Step 3: Write down the square root of the perfect square found in step 2. In this case, the square root of 25 is 5.

Step 4: Subtract the product of the square root found in step 3 and the divisor (5) from the first group of digits (31) to get the remainder. In this case, subtract 25 from 31, leaving a remainder of 6.

Step 5: Bring down the next pair of digits (428) and double the value of the square root found in step 3 (5). We now have 54.

Step 6: Find the largest digit 'x' such that when the value 2 * (10A + x) is multiplied by x, the result is less than or equal to the number formed by the remainder and the next pair of digits (6 and 428 in this case).

Step 7: Write down the value of 'x' found in step 6 as the next digit of the square root. In this case, the largest value of 'x' is 2 because 2 * (10*5 + 2) equals 104, which is less than 6428.

Step 8: Multiply the current divisor (52) by the value of 'x' found in step 7, which gives 2 * 52 = 104.

Step 9: Subtract the product found in step 8 (104) from the number formed by the remainder and the next pair of digits (6428) to get the new remainder. In this case, subtracting 104 from 6428 leaves a remainder of 6324.

Step 10: Bring down the next pair of digits (324) and double the current divisor (52) to get 104.

Step 11: Repeat steps 6 to 9 until all the digits have been brought down.

Step 12: Once you have brought down all the digits, continue the process by adding a decimal point after the digit found in step 3 (which was 5 in this case).

Therefore, the square root of 0.31428 using the division method is approximately 0.56047.